Subgroups — C₂×C₇×#3505 #13239983

Order 1792.

8082 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3505	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#553	C₂	1	4	yes	maximal, complemented
4	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#551	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#548	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#546	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#539	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#538	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#534	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#518	C₂	1	2	yes	maximal, complemented
16	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	2	yes	complemented
18	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₇×D₄	C₂²	1	2	yes	—
21	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
24	C₇×#553	C₂²	1	32	yes	complemented
25	C₇×#553	C₂²	1	64	yes	complemented
26	C₇×#552	C₂²	1	32	yes	complemented
27	C₇×#551	C₂²	1	64	yes	complemented
28	C₇×#548	C₂²	1	32	yes	complemented
29	C₇×#546	C₂²	1	32	yes	complemented
30	C₇×#539	C₂²	1	32	yes	complemented
31	C₇×#538	C₂²	1	32	yes	complemented
32	C₇×#534	C₂²	1	32	yes	complemented
33	C₇×#529	C₂²	1	32	yes	complemented
34	C₂×C₇×#126	C₂²	1	4	yes	complemented
35	C₂×C₇×#126	C₂²	1	4	yes	complemented
36	C₂×C₇×#126	C₂²	1	4	yes	complemented
37	C₂×C₇×#125	C₂²	1	2	yes	complemented
38	C₂×C₇×#125	C₂²	1	4	yes	complemented
39	C₂×C₇×#124	C₂²	1	2	yes	complemented
40	C₂×C₇×#124	C₂²	1	4	yes	complemented
41	C₇×#525	C₂²	1	32	yes	complemented
42	C₂×C₇×#123	C₂²	1	4	yes	—
43	C₂×C₇×#123	C₂²	1	4	yes	complemented
44	C₂×C₇×#123	C₂²	1	4	yes	complemented
45	C₂×C₇×#123	C₂²	1	4	yes	complemented
46	C₂×C₇×#123	C₂²	1	4	yes	complemented
47	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
48	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
49	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
50	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
51	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
52	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
53	C₂×C₇×C₂²⋊Q₈	C₂²	1	16	yes	complemented
54	C₂×C₇×#121	C₂²	1	2	yes	—
55	C₂×C₇×#121	C₂²	1	2	yes	—
56	C₂×C₇×#121	C₂²	1	2	yes	complemented
57	C₂×C₇×#121	C₂²	1	2	yes	complemented
58	C₂×C₇×#121	C₂²	1	2	yes	complemented
59	C₂×C₇×#121	C₂²	1	4	yes	complemented
60	C₂×C₇×#121	C₂²	1	4	yes	complemented
61	C₂×C₇×#121	C₂²	1	4	yes	complemented
62	C₂×C₇×#121	C₂²	1	16	yes	complemented
63	C₂×C₇×#120	C₂²	1	4	yes	—
64	C₂×C₇×#120	C₂²	1	4	yes	complemented
65	C₇×#518	C₂²	1	32	yes	complemented
66	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
67	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
68	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
69	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
70	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
71	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
72	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
73	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
74	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
75	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
76	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
77	C₂×C₄×C₇×D₄	C₂²	1	16	yes	complemented
78	C₂×C₇×#117	C₂²	1	4	yes	complemented
79	C₂×C₇×#117	C₂²	1	2	yes	complemented
80	C₂×C₇×#117	C₂²	1	4	yes	complemented
81	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
84	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
85	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
87	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
89	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
90	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
91	C₂×#3505	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁵×C₇	C₂³	1	2	yes	—
93	C₂⁵×C₇	C₂³	1	1	yes	characteristic
94	C₂⁵×C₇	C₂³	1	1	yes	characteristic
95	C₂×C₇×#41	—	4	8	no	—
96	C₂×C₇×#41	C₂³	1	16	yes	complemented
97	C₂²×C₇×Q₈	—	4	4	no	—
98	C₂²×C₇×Q₈	C₂³	1	2	yes	—
99	C₂²×C₇×Q₈	C₂³	1	2	yes	—
100	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
101	C₂²×C₇×D₄	—	2	8	no	—
102	C₂²×C₇×D₄	—	2	16	no	—
103	C₂²×C₇×D₄	—	4	4	no	—
104	C₂²×C₇×D₄	C₂³	1	2	yes	—
105	C₂²×C₇×D₄	C₂³	1	4	yes	—
106	C₂²×C₇×D₄	C₂³	1	2	yes	—
107	C₂²×C₇×D₄	C₂³	1	4	yes	—
108	C₂²×C₇×D₄	C₂³	1	8	yes	—
109	C₂²×C₇×D₄	C₂³	1	16	yes	—
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂²×C₇×D₄	C₂³	1	2	yes	—
112	C₂²×C₇×D₄	C₂³	1	4	yes	—
113	C₂²×C₇×D₄	C₂³	1	4	yes	—
114	C₂²×C₇×D₄	C₂³	1	8	yes	complemented
115	C₂³×C₄×C₇	—	4	4	no	—
116	C₂³×C₄×C₇	—	4	4	no	—
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₇	C₂³	1	4	yes	—
125	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇	C₂³	1	4	yes	—
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	8	yes	—
134	C₂³×C₄×C₇	C₂³	1	8	yes	complemented
135	C₇×#126	C₂³	1	32	yes	complemented
136	C₇×#126	C₂³	1	32	yes	complemented
137	C₇×#126	C₂³	1	32	yes	complemented
138	C₇×#125	C₂³	1	16	yes	complemented
139	C₇×#125	C₂³	1	32	yes	complemented
140	C₇×#124	C₂³	1	16	yes	complemented
141	C₇×#124	C₂³	1	32	yes	complemented
142	C₇×#123	C₂³	1	32	yes	—
143	C₇×#123	C₂³	1	32	yes	complemented
144	C₇×#123	C₂³	1	32	yes	complemented
145	C₇×#123	C₂³	1	32	yes	complemented
146	C₇×#123	C₂³	1	32	yes	complemented
147	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
148	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
149	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
150	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
152	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	C₇×#121	C₂³	1	16	yes	—
154	C₇×#121	C₂³	1	16	yes	—
155	C₇×#121	C₂³	1	16	yes	complemented
156	C₇×#121	C₂³	1	16	yes	complemented
157	C₇×#121	C₂³	1	16	yes	complemented
158	C₇×#121	C₂³	1	32	yes	complemented
159	C₇×#121	C₂³	1	32	yes	complemented
160	C₇×#121	C₂³	1	32	yes	complemented
161	C₇×#120	C₂³	1	32	yes	—
162	C₇×#120	C₂³	1	32	yes	complemented
163	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
164	C₄×C₇×D₄	C₂³	1	16	yes	—
165	C₄×C₇×D₄	C₂³	1	16	yes	—
166	C₄×C₇×D₄	C₂³	1	16	yes	complemented
167	C₄×C₇×D₄	C₂³	1	16	yes	complemented
168	C₄×C₇×D₄	C₂³	1	32	yes	complemented
169	C₄×C₇×D₄	C₂³	1	32	yes	complemented
170	C₄×C₇×D₄	C₂³	1	32	yes	complemented
171	C₄×C₇×D₄	C₂³	1	32	yes	complemented
172	C₄×C₇×D₄	C₂³	1	32	yes	complemented
173	C₄×C₇×D₄	C₂³	1	16	yes	complemented
174	C₇×#117	C₂³	1	32	yes	complemented
175	C₇×#117	C₂³	1	16	yes	complemented
176	C₇×#117	C₂³	1	32	yes	complemented
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
190	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
191	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
192	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	4	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×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
209	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	complemented
210	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
211	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	complemented
212	C₂×C₄²×C₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₇	C₂³	1	4	yes	—
215	C₂×C₄²×C₇	C₂³	1	4	yes	—
216	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
217	#3505	C₂×C₇	1	32	yes	direct product factor
218	C₂×#553	C₂×C₇	1	2	yes	complemented
219	C₂×#553	C₂×C₇	1	4	yes	complemented
220	C₂×#552	C₂×C₇	1	2	yes	complemented
221	C₂×#551	C₂×C₇	1	4	yes	complemented
222	C₂×#548	C₂×C₇	1	2	yes	complemented
223	C₂×#546	C₂×C₇	1	2	yes	complemented
224	C₂×#539	C₂×C₇	1	2	yes	complemented
225	C₂×#538	C₂×C₇	1	2	yes	complemented
226	C₂×#534	C₂×C₇	1	2	yes	complemented
227	C₂×#529	C₂×C₇	1	2	yes	complemented
228	C₂×#525	C₂×C₇	1	2	yes	complemented
229	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
230	C₂²×#121	C₂×C₇	1	1	yes	characteristic, complemented
231	C₂×#518	C₂×C₇	1	2	yes	complemented
232	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
233	C₂⁴×C₇	—	2	4	no	—
234	C₂⁴×C₇	—	2	8	no	—
235	C₂⁴×C₇	—	4	2	no	—
236	C₂⁴×C₇	—	4	2	no	—
237	C₂⁴×C₇	—	4	2	no	—
238	C₂⁴×C₇	—	4	2	no	—
239	C₂⁴×C₇	—	4	4	no	—
240	C₂⁴×C₇	—	4	4	no	—
241	C₂⁴×C₇	#41	1	8	yes	complemented
242	C₂⁴×C₇	C₂⁴	1	2	yes	—
243	C₂⁴×C₇	C₂⁴	1	4	yes	—
244	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
246	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₇	C₂⁴	1	8	yes	—
248	C₂⁴×C₇	C₂⁴	1	4	yes	—
249	C₂⁴×C₇	C₂⁴	1	4	yes	—
250	C₇×#41	—	4	32	no	—
251	C₂×C₇×Q₈	—	2	8	no	—
252	C₂×C₇×Q₈	—	4	4	no	—
253	C₂×C₇×Q₈	—	4	16	no	—
254	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
255	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
256	C₂×C₇×D₄	—	2	8	no	—
257	C₂×C₇×D₄	—	2	16	no	—
258	C₂×C₇×D₄	—	2	8	no	—
259	C₂×C₇×D₄	—	2	16	no	—
260	C₂×C₇×D₄	—	2	32	no	—
261	C₂×C₇×D₄	—	2	64	no	—
262	C₂×C₇×D₄	—	2	8	no	—
263	C₂×C₇×D₄	—	4	16	no	—
264	C₂×C₇×D₄	—	4	4	no	—
265	C₂×C₇×D₄	—	4	8	no	—
266	C₂×C₇×D₄	—	4	8	no	—
267	C₂×C₇×D₄	C₂⁴	1	8	yes	—
268	C₂×C₇×D₄	C₂⁴	1	16	yes	—
269	C₂×C₇×D₄	C₂⁴	1	8	yes	—
270	C₂×C₇×D₄	C₂⁴	1	16	yes	—
271	C₂×C₇×D₄	C₂⁴	1	8	yes	—
272	C₂×C₇×D₄	C₂⁴	1	16	yes	—
273	C₂×C₇×D₄	C₂⁴	1	16	yes	—
274	C₂×C₇×D₄	C₂⁴	1	8	yes	—
275	C₂²×C₄×C₇	—	2	8	no	—
276	C₂²×C₄×C₇	—	2	4	no	—
277	C₂²×C₄×C₇	—	2	4	no	—
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	—	4	16	no	—
282	C₂²×C₄×C₇	—	4	16	no	—
283	C₂²×C₄×C₇	—	4	2	no	—
284	C₂²×C₄×C₇	—	4	4	no	—
285	C₂²×C₄×C₇	—	4	2	no	—
286	C₂²×C₄×C₇	—	4	2	no	—
287	C₂²×C₄×C₇	—	4	2	no	—
288	C₂²×C₄×C₇	—	4	2	no	—
289	C₂²×C₄×C₇	—	4	8	no	—
290	C₂²×C₄×C₇	—	4	4	no	—
291	C₂²×C₄×C₇	—	4	4	no	—
292	C₂²×C₄×C₇	—	4	8	no	—
293	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
311	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	8	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
330	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
331	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
332	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
333	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
335	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
337	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
338	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
339	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
340	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
341	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
342	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
343	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
344	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
345	C₄²×C₇	C₂⁴	1	8	yes	—
346	C₄²×C₇	C₂⁴	1	8	yes	—
347	C₄²×C₇	C₂⁴	1	16	yes	—
348	C₄²×C₇	C₂⁴	1	16	yes	—
349	C₂²×#41	C₂²×C₇	1	2	yes	complemented
350	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
351	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
352	C₂³×D₄	C₂²×C₇	1	2	yes	—
353	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
354	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
355	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
356	#553	C₂²×C₇	1	32	yes	complemented
357	#553	C₂²×C₇	1	64	yes	complemented
358	#552	C₂²×C₇	1	32	yes	complemented
359	#551	C₂²×C₇	1	64	yes	complemented
360	#548	C₂²×C₇	1	32	yes	complemented
361	#546	C₂²×C₇	1	32	yes	complemented
362	#539	C₂²×C₇	1	32	yes	complemented
363	#538	C₂²×C₇	1	32	yes	complemented
364	#534	C₂²×C₇	1	32	yes	complemented
365	#529	C₂²×C₇	1	32	yes	complemented
366	C₂×#126	C₂²×C₇	1	4	yes	complemented
367	C₂×#126	C₂²×C₇	1	4	yes	complemented
368	C₂×#126	C₂²×C₇	1	4	yes	complemented
369	C₂×#125	C₂²×C₇	1	2	yes	complemented
370	C₂×#125	C₂²×C₇	1	4	yes	complemented
371	C₂×#124	C₂²×C₇	1	2	yes	complemented
372	C₂×#124	C₂²×C₇	1	4	yes	complemented
373	#525	C₂²×C₇	1	32	yes	complemented
374	C₂×#123	C₂²×C₇	1	4	yes	—
375	C₂×#123	C₂²×C₇	1	4	yes	complemented
376	C₂×#123	C₂²×C₇	1	4	yes	complemented
377	C₂×#123	C₂²×C₇	1	4	yes	complemented
378	C₂×#123	C₂²×C₇	1	4	yes	complemented
379	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
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	2	yes	complemented
383	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
384	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
385	C₂×C₂²⋊Q₈	C₂²×C₇	1	16	yes	complemented
386	C₂×#121	C₂²×C₇	1	2	yes	—
387	C₂×#121	C₂²×C₇	1	2	yes	—
388	C₂×#121	C₂²×C₇	1	2	yes	complemented
389	C₂×#121	C₂²×C₇	1	2	yes	complemented
390	C₂×#121	C₂²×C₇	1	2	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	16	yes	complemented
395	C₂×#120	C₂²×C₇	1	4	yes	—
396	C₂×#120	C₂²×C₇	1	4	yes	complemented
397	#518	C₂²×C₇	1	32	yes	complemented
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	2	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×C₄×D₄	C₂²×C₇	1	4	yes	complemented
406	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
407	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
408	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
409	C₂×C₄×D₄	C₂²×C₇	1	16	yes	complemented
410	C₂×#117	C₂²×C₇	1	4	yes	complemented
411	C₂×#117	C₂²×C₇	1	2	yes	complemented
412	C₂×#117	C₂²×C₇	1	4	yes	complemented
413	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
414	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
415	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
416	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
417	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
418	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
419	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
420	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
421	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
422	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
423	C₂³×C₇	—	2	2	no	—
424	C₂³×C₇	—	2	2	no	—
425	C₂³×C₇	—	2	2	no	—
426	C₂³×C₇	—	2	2	no	—
427	C₂³×C₇	—	2	2	no	—
428	C₂³×C₇	—	2	2	no	—
429	C₂³×C₇	—	2	8	no	—
430	C₂³×C₇	—	2	4	no	—
431	C₂³×C₇	—	2	8	no	—
432	C₂³×C₇	—	2	4	no	—
433	C₂³×C₇	—	2	8	no	—
434	C₂³×C₇	—	2	8	no	—
435	C₂³×C₇	—	2	4	no	—
436	C₂³×C₇	—	2	16	no	—
437	C₂³×C₇	—	4	4	no	—
438	C₂³×C₇	—	4	4	no	—
439	C₂³×C₇	—	4	16	no	—
440	C₂³×C₇	—	4	4	no	—
441	C₂³×C₇	—	4	4	no	—
442	C₂³×C₇	—	4	8	no	—
443	C₂³×C₇	—	4	8	no	—
444	C₂³×C₇	—	4	16	no	—
445	C₂³×C₇	—	8	16	no	—
446	C₂³×C₇	C₂×#41	1	4	yes	—
447	C₂³×C₇	C₂×#41	1	4	yes	—
448	C₂³×C₇	C₂×#41	1	4	yes	—
449	C₂³×C₇	C₂×#41	1	16	yes	complemented
450	C₂³×C₇	C₂⁵	1	4	yes	—
451	C₂³×C₇	C₂⁵	1	8	yes	—
452	C₂³×C₇	C₂⁵	1	2	yes	—
453	C₂³×C₇	C₂⁵	1	2	yes	—
454	C₂³×C₇	C₂⁵	1	2	yes	—
455	C₂³×C₇	C₂⁵	1	1	yes	characteristic
456	C₇×Q₈	—	2	16	no	—
457	C₇×Q₈	—	4	8	no	—
458	C₇×D₄	—	2	16	no	—
459	C₇×D₄	—	2	32	no	—
460	C₇×D₄	—	2	16	no	—
461	C₇×D₄	—	2	32	no	—
462	C₇×D₄	—	2	16	no	—
463	C₇×D₄	—	4	8	no	—
464	C₇×D₄	—	4	16	no	—
465	C₇×D₄	—	4	16	no	—
466	C₂×C₄×C₇	—	2	16	no	—
467	C₂×C₄×C₇	—	2	8	no	—
468	C₂×C₄×C₇	—	2	8	no	—
469	C₂×C₄×C₇	—	2	4	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	4	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	8	no	—
475	C₂×C₄×C₇	—	2	4	no	—
476	C₂×C₄×C₇	—	2	8	no	—
477	C₂×C₄×C₇	—	2	8	no	—
478	C₂×C₄×C₇	—	2	8	no	—
479	C₂×C₄×C₇	—	2	8	no	—
480	C₂×C₄×C₇	—	2	16	no	—
481	C₂×C₄×C₇	—	4	4	no	—
482	C₂×C₄×C₇	—	4	8	no	—
483	C₂×C₄×C₇	—	4	4	no	—
484	C₂×C₄×C₇	—	4	4	no	—
485	C₂×C₄×C₇	—	4	4	no	—
486	C₂×C₄×C₇	—	4	4	no	—
487	C₂×C₄×C₇	—	4	16	no	—
488	C₂×C₄×C₇	—	4	8	no	—
489	C₂×C₄×C₇	—	4	8	no	—
490	C₂×C₄×C₇	—	4	16	no	—
491	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
492	C₂×C₄×C₇	C₂⁵	1	4	yes	—
493	C₂×C₄×C₇	C₂⁵	1	4	yes	—
494	C₂×C₄×C₇	C₂⁵	1	8	yes	—
495	C₂×C₄×C₇	C₂⁵	1	2	yes	—
496	C₂×C₄×C₇	C₂⁵	1	4	yes	—
497	C₂×C₄×C₇	C₂⁵	1	8	yes	—
498	C₂×C₄×C₇	C₂⁵	1	8	yes	—
499	C₂×C₄×C₇	C₂⁵	1	2	yes	—
500	C₂×C₄×C₇	C₂⁵	1	2	yes	—
501	C₂×C₄×C₇	C₂⁵	1	2	yes	—
502	C₂⁵	C₂³×C₇	1	2	yes	—
503	C₂⁵	C₂³×C₇	1	1	yes	characteristic
504	C₂⁵	C₂³×C₇	1	1	yes	characteristic
505	C₂×#41	—	4	8	no	—
506	C₂×#41	C₂³×C₇	1	16	yes	complemented
507	C₂²×Q₈	—	4	4	no	—
508	C₂²×Q₈	C₂³×C₇	1	2	yes	—
509	C₂²×Q₈	C₂³×C₇	1	2	yes	—
510	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
511	C₂²×D₄	—	2	8	no	—
512	C₂²×D₄	—	2	16	no	—
513	C₂²×D₄	—	4	4	no	—
514	C₂²×D₄	C₂³×C₇	1	2	yes	—
515	C₂²×D₄	C₂³×C₇	1	4	yes	—
516	C₂²×D₄	C₂³×C₇	1	2	yes	—
517	C₂²×D₄	C₂³×C₇	1	4	yes	—
518	C₂²×D₄	C₂³×C₇	1	8	yes	—
519	C₂²×D₄	C₂³×C₇	1	2	yes	—
520	C₂²×D₄	C₂³×C₇	1	16	yes	—
521	C₂²×D₄	C₂³×C₇	1	4	yes	—
522	C₂²×D₄	C₂³×C₇	1	4	yes	—
523	C₂²×D₄	C₂³×C₇	1	2	yes	—
524	C₂²×D₄	C₂³×C₇	1	8	yes	complemented
525	C₂³×C₄	—	4	4	no	—
526	C₂³×C₄	—	4	4	no	—
527	C₂³×C₄	C₂³×C₇	1	2	yes	—
528	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₇	1	2	yes	—
532	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₇	1	2	yes	—
535	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₇	1	2	yes	—
537	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₇	1	4	yes	—
540	C₂³×C₄	C₂³×C₇	1	4	yes	—
541	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₇	1	2	yes	—
543	C₂³×C₄	C₂³×C₇	1	8	yes	—
544	C₂³×C₄	C₂³×C₇	1	8	yes	complemented
545	#126	C₂³×C₇	1	32	yes	complemented
546	#126	C₂³×C₇	1	32	yes	complemented
547	#126	C₂³×C₇	1	32	yes	complemented
548	#125	C₂³×C₇	1	16	yes	complemented
549	#125	C₂³×C₇	1	32	yes	complemented
550	#124	C₂³×C₇	1	16	yes	complemented
551	#124	C₂³×C₇	1	32	yes	complemented
552	#123	C₂³×C₇	1	32	yes	—
553	#123	C₂³×C₇	1	32	yes	complemented
554	#123	C₂³×C₇	1	32	yes	complemented
555	#123	C₂³×C₇	1	32	yes	complemented
556	#123	C₂³×C₇	1	32	yes	complemented
557	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
558	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
559	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
560	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
561	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
562	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
563	#121	C₂³×C₇	1	16	yes	—
564	#121	C₂³×C₇	1	16	yes	—
565	#121	C₂³×C₇	1	16	yes	complemented
566	#121	C₂³×C₇	1	16	yes	complemented
567	#121	C₂³×C₇	1	16	yes	complemented
568	#121	C₂³×C₇	1	32	yes	complemented
569	#121	C₂³×C₇	1	32	yes	complemented
570	#121	C₂³×C₇	1	32	yes	complemented
571	#120	C₂³×C₇	1	32	yes	—
572	#120	C₂³×C₇	1	32	yes	complemented
573	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
574	C₄×D₄	C₂³×C₇	1	16	yes	—
575	C₄×D₄	C₂³×C₇	1	16	yes	—
576	C₄×D₄	C₂³×C₇	1	16	yes	complemented
577	C₄×D₄	C₂³×C₇	1	16	yes	complemented
578	C₄×D₄	C₂³×C₇	1	32	yes	complemented
579	C₄×D₄	C₂³×C₇	1	32	yes	complemented
580	C₄×D₄	C₂³×C₇	1	32	yes	complemented
581	C₄×D₄	C₂³×C₇	1	32	yes	complemented
582	C₄×D₄	C₂³×C₇	1	32	yes	complemented
583	C₄×D₄	C₂³×C₇	1	16	yes	complemented
584	#117	C₂³×C₇	1	32	yes	complemented
585	#117	C₂³×C₇	1	16	yes	complemented
586	#117	C₂³×C₇	1	32	yes	complemented
587	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
596	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
597	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
600	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
601	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
602	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
603	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	complemented
620	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
621	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	complemented
622	C₂×C₄²	C₂³×C₇	1	2	yes	—
623	C₂×C₄²	C₂³×C₇	1	4	yes	—
624	C₂×C₄²	C₂³×C₇	1	4	yes	—
625	C₂×C₄²	C₂³×C₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
627	C₂²×C₇	—	2	2	no	—
628	C₂²×C₇	—	2	2	no	—
629	C₂²×C₇	—	2	2	no	—
630	C₂²×C₇	—	2	2	no	—
631	C₂²×C₇	—	2	2	no	—
632	C₂²×C₇	—	2	2	no	—
633	C₂²×C₇	—	2	8	no	—
634	C₂²×C₇	—	2	8	no	—
635	C₂²×C₇	—	2	8	no	—
636	C₂²×C₇	—	2	4	no	—
637	C₂²×C₇	—	2	8	no	—
638	C₂²×C₇	—	2	4	no	—
639	C₂²×C₇	—	2	8	no	—
640	C₂²×C₇	—	2	8	no	—
641	C₂²×C₇	—	2	4	no	—
642	C₂²×C₇	—	4	16	no	—
643	C₂²×C₇	—	4	16	no	—
644	C₂²×C₇	—	4	8	no	—
645	C₂²×C₇	—	4	16	no	—
646	C₂²×C₇	—	8	16	no	—
647	C₂²×C₇	C₂²×#41	1	4	yes	—
648	C₂²×C₇	C₂²×#41	1	4	yes	—
649	C₂²×C₇	C₂²×#41	1	4	yes	—
650	C₂²×C₇	C₂²×#41	1	2	yes	—
651	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
652	C₂²×C₇	#585	1	2	yes	—
653	C₂²×C₇	C₂⁶	1	1	yes	characteristic
654	C₄×C₇	—	2	8	no	—
655	C₄×C₇	—	2	4	no	—
656	C₄×C₇	—	2	2	no	—
657	C₄×C₇	—	2	4	no	—
658	C₄×C₇	—	2	2	no	—
659	C₄×C₇	—	2	2	no	—
660	C₄×C₇	—	2	8	no	—
661	C₄×C₇	—	2	4	no	—
662	C₄×C₇	—	2	8	no	—
663	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
664	C₂⁴	—	2	4	no	—
665	C₂⁴	—	2	8	no	—
666	C₂⁴	—	4	2	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	—	4	2	no	—
669	C₂⁴	—	4	2	no	—
670	C₂⁴	—	4	4	no	—
671	C₂⁴	—	4	4	no	—
672	C₂⁴	C₇×#41	1	8	yes	complemented
673	C₂⁴	C₂⁴×C₇	1	2	yes	—
674	C₂⁴	C₂⁴×C₇	1	4	yes	—
675	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
676	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
677	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₇	1	8	yes	—
679	C₂⁴	C₂⁴×C₇	1	4	yes	—
680	C₂⁴	C₂⁴×C₇	1	4	yes	—
681	#41	—	4	32	no	—
682	C₂×Q₈	—	2	8	no	—
683	C₂×Q₈	—	4	4	no	—
684	C₂×Q₈	—	4	16	no	—
685	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
686	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
687	C₂×D₄	—	2	8	no	—
688	C₂×D₄	—	2	16	no	—
689	C₂×D₄	—	2	8	no	—
690	C₂×D₄	—	2	16	no	—
691	C₂×D₄	—	2	32	no	—
692	C₂×D₄	—	2	64	no	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	4	16	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	8	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	C₂⁴×C₇	1	8	yes	—
699	C₂×D₄	C₂⁴×C₇	1	16	yes	—
700	C₂×D₄	C₂⁴×C₇	1	8	yes	—
701	C₂×D₄	C₂⁴×C₇	1	16	yes	—
702	C₂×D₄	C₂⁴×C₇	1	8	yes	—
703	C₂×D₄	C₂⁴×C₇	1	16	yes	—
704	C₂×D₄	C₂⁴×C₇	1	16	yes	—
705	C₂×D₄	C₂⁴×C₇	1	8	yes	—
706	C₂²×C₄	—	2	8	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	8	no	—
712	C₂²×C₄	—	4	16	no	—
713	C₂²×C₄	—	4	16	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	4	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	4	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	8	no	—
722	C₂²×C₄	—	4	4	no	—
723	C₂²×C₄	—	4	8	no	—
724	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
727	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
730	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
731	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
733	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
736	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
737	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
738	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
739	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
741	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
742	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
743	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
745	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
746	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
749	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
750	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
751	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
752	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
753	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
754	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
755	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
756	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
757	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
758	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
759	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
761	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
762	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
763	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
764	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
765	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
766	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
767	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
768	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
769	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
770	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
771	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
772	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
773	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
774	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
775	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
776	C₄²	C₂⁴×C₇	1	8	yes	—
777	C₄²	C₂⁴×C₇	1	8	yes	—
778	C₄²	C₂⁴×C₇	1	16	yes	—
779	C₄²	C₂⁴×C₇	1	16	yes	—
780	C₂×C₇	—	2	4	no	—
781	C₂×C₇	—	2	4	no	—
782	C₂×C₇	—	2	4	no	—
783	C₂×C₇	—	4	4	no	—
784	C₂×C₇	—	4	8	no	—
785	C₂×C₇	#3505	1	4	yes	direct product factor
786	C₂×C₇	C₂³×#41	1	1	yes	characteristic
787	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
788	C₂×C₇	C₂×#585	1	1	yes	characteristic
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	8	no	—
796	C₂³	—	2	4	no	—
797	C₂³	—	2	8	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	8	no	—
800	C₂³	—	2	8	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	16	no	—
803	C₂³	—	4	4	no	—
804	C₂³	—	4	4	no	—
805	C₂³	—	4	16	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	4	4	no	—
808	C₂³	—	4	8	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	4	16	no	—
811	C₂³	—	8	16	no	—
812	C₂³	C₂×C₇×#41	1	4	yes	—
813	C₂³	C₂×C₇×#41	1	4	yes	—
814	C₂³	C₂×C₇×#41	1	4	yes	—
815	C₂³	C₂×C₇×#41	1	16	yes	complemented
816	C₂³	C₂⁵×C₇	1	4	yes	—
817	C₂³	C₂⁵×C₇	1	8	yes	—
818	C₂³	C₂⁵×C₇	1	2	yes	—
819	C₂³	C₂⁵×C₇	1	2	yes	—
820	C₂³	C₂⁵×C₇	1	2	yes	—
821	C₂³	C₂⁵×C₇	1	1	yes	characteristic
822	Q₈	—	2	16	no	—
823	Q₈	—	4	8	no	—
824	D₄	—	2	16	no	—
825	D₄	—	2	32	no	—
826	D₄	—	2	16	no	—
827	D₄	—	2	32	no	—
828	D₄	—	2	16	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	16	no	—
831	D₄	—	4	16	no	—
832	C₂×C₄	—	2	16	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	8	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	8	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	16	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	16	no	—
857	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
858	C₂×C₄	C₂⁵×C₇	1	4	yes	—
859	C₂×C₄	C₂⁵×C₇	1	4	yes	—
860	C₂×C₄	C₂⁵×C₇	1	8	yes	—
861	C₂×C₄	C₂⁵×C₇	1	2	yes	—
862	C₂×C₄	C₂⁵×C₇	1	4	yes	—
863	C₂×C₄	C₂⁵×C₇	1	8	yes	—
864	C₂×C₄	C₂⁵×C₇	1	8	yes	—
865	C₂×C₄	C₂⁵×C₇	1	2	yes	—
866	C₂×C₄	C₂⁵×C₇	1	2	yes	—
867	C₂×C₄	C₂⁵×C₇	1	2	yes	—
868	C₇	C₂×#3505	1	1	yes	characteristic, direct product factor, Sylow
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	8	no	—
876	C₂²	—	2	8	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	8	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	4	16	no	—
885	C₂²	—	4	16	no	—
886	C₂²	—	4	8	no	—
887	C₂²	—	4	16	no	—
888	C₂²	—	8	16	no	—
889	C₂²	C₂²×C₇×#41	1	4	yes	—
890	C₂²	C₂²×C₇×#41	1	4	yes	—
891	C₂²	C₂²×C₇×#41	1	4	yes	—
892	C₂²	C₂²×C₇×#41	1	2	yes	—
893	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
894	C₂²	C₇×#585	1	2	yes	—
895	C₂²	C₂⁶×C₇	1	1	yes	characteristic
896	C₄	—	2	8	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	8	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	8	no	—
905	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
906	C₂	—	2	4	no	—
907	C₂	—	2	4	no	—
908	C₂	—	2	4	no	—
909	C₂	—	4	4	no	—
910	C₂	—	4	8	no	—
911	C₂	C₇×#3505	1	4	yes	direct product factor
912	C₂	C₂³×C₇×#41	1	1	yes	characteristic
913	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
914	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×#3505	C₂	direct (N × H)
2. C₂×C₇×#553	C₂	semidirect
3. C₂×C₇×#553	C₂	semidirect
4. C₂×C₇×#552	C₂	semidirect
5. C₂×C₇×#551	C₂	semidirect
6. C₂×C₇×#548	C₂	semidirect
7. C₂×C₇×#546	C₂	semidirect
8. C₂×C₇×#539	C₂	semidirect
9. C₂×C₇×#538	C₂	semidirect
10. C₂×C₇×#534	C₂	semidirect
11. C₂×C₇×#529	C₂	semidirect
12. C₂×C₇×#525	C₂	semidirect
13. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
14. C₂²×C₇×#121	C₂	semidirect
15. C₂×C₇×#518	C₂	semidirect
16. C₂²×C₄×C₇×D₄	C₂	semidirect
17. C₂²×C₇×#41	C₂²	semidirect
18. C₂³×C₇×Q₈	C₂²	semidirect
21. C₂³×C₇×D₄	C₂²	semidirect
23. C₂⁴×C₄×C₇	C₂²	semidirect
24. C₇×#553	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×#539	C₂²	semidirect
31. C₇×#538	C₂²	semidirect
32. C₇×#534	C₂²	semidirect
33. C₇×#529	C₂²	semidirect
34. C₂×C₇×#126	C₂²	semidirect
35. C₂×C₇×#126	C₂²	semidirect
36. C₂×C₇×#126	C₂²	semidirect
37. C₂×C₇×#125	C₂²	semidirect
38. C₂×C₇×#125	C₂²	semidirect
39. C₂×C₇×#124	C₂²	semidirect
40. C₂×C₇×#124	C₂²	semidirect
41. C₇×#525	C₂²	semidirect
43. C₂×C₇×#123	C₂²	semidirect
44. C₂×C₇×#123	C₂²	semidirect
45. C₂×C₇×#123	C₂²	semidirect
46. C₂×C₇×#123	C₂²	semidirect
47. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
50. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
51. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
52. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₇×#121	C₂²	semidirect
57. C₂×C₇×#121	C₂²	semidirect
58. C₂×C₇×#121	C₂²	semidirect
59. C₂×C₇×#121	C₂²	semidirect
60. C₂×C₇×#121	C₂²	semidirect
61. C₂×C₇×#121	C₂²	semidirect
62. C₂×C₇×#121	C₂²	semidirect
64. C₂×C₇×#120	C₂²	semidirect
65. C₇×#518	C₂²	semidirect
66. C₂×C₄×C₇×Q₈	C₂²	semidirect
69. C₂×C₄×C₇×D₄	C₂²	semidirect
70. C₂×C₄×C₇×D₄	C₂²	semidirect
71. C₂×C₄×C₇×D₄	C₂²	semidirect
72. C₂×C₄×C₇×D₄	C₂²	semidirect
73. C₂×C₄×C₇×D₄	C₂²	semidirect
74. C₂×C₄×C₇×D₄	C₂²	semidirect
75. C₂×C₄×C₇×D₄	C₂²	semidirect
76. C₂×C₄×C₇×D₄	C₂²	semidirect
77. C₂×C₄×C₇×D₄	C₂²	semidirect
78. C₂×C₇×#117	C₂²	semidirect
79. C₂×C₇×#117	C₂²	semidirect
80. C₂×C₇×#117	C₂²	semidirect
81. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
82. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
83. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
84. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
87. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
88. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
89. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
90. C₂²×C₄²×C₇	C₂²	semidirect
91. C₂×#3505	C₇	direct (N × H)
96. C₂×C₇×#41	C₂³	semidirect
100. C₂²×C₇×Q₈	C₂³	semidirect
114. C₂²×C₇×D₄	C₂³	semidirect
134. C₂³×C₄×C₇	C₂³	semidirect
135. C₇×#126	C₂³	semidirect
136. C₇×#126	C₂³	semidirect
137. C₇×#126	C₂³	semidirect
138. C₇×#125	C₂³	semidirect
139. C₇×#125	C₂³	semidirect
140. C₇×#124	C₂³	semidirect
141. C₇×#124	C₂³	semidirect
143. C₇×#123	C₂³	semidirect
144. C₇×#123	C₂³	semidirect
145. C₇×#123	C₂³	semidirect
146. C₇×#123	C₂³	semidirect
147. C₇×C₂²⋊Q₈	C₂³	semidirect
148. C₇×C₂²⋊Q₈	C₂³	semidirect
149. C₇×C₂²⋊Q₈	C₂³	semidirect
150. C₇×C₂²⋊Q₈	C₂³	semidirect
151. C₇×C₂²⋊Q₈	C₂³	semidirect
152. C₇×C₂²⋊Q₈	C₂³	semidirect
155. C₇×#121	C₂³	semidirect
156. C₇×#121	C₂³	semidirect
157. C₇×#121	C₂³	semidirect
158. C₇×#121	C₂³	semidirect
159. C₇×#121	C₂³	semidirect
160. C₇×#121	C₂³	semidirect
162. C₇×#120	C₂³	semidirect
163. C₄×C₇×Q₈	C₂³	semidirect
166. C₄×C₇×D₄	C₂³	semidirect
167. C₄×C₇×D₄	C₂³	semidirect
168. C₄×C₇×D₄	C₂³	semidirect
169. C₄×C₇×D₄	C₂³	semidirect
170. C₄×C₇×D₄	C₂³	semidirect
171. C₄×C₇×D₄	C₂³	semidirect
172. C₄×C₇×D₄	C₂³	semidirect
173. C₄×C₇×D₄	C₂³	semidirect
174. C₇×#117	C₂³	semidirect
175. C₇×#117	C₂³	semidirect
176. C₇×#117	C₂³	semidirect
189. C₂×C₇×C₄⋊C₄	C₂³	semidirect
190. C₂×C₇×C₄⋊C₄	C₂³	semidirect
191. C₂×C₇×C₄⋊C₄	C₂³	semidirect
192. C₂×C₇×C₄⋊C₄	C₂³	semidirect
209. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
210. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
211. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
216. C₂×C₄²×C₇	C₂³	semidirect
217. #3505	C₂×C₇	direct (N × H)
218. C₂×#553	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×#539	C₂×C₇	semidirect
225. C₂×#538	C₂×C₇	semidirect
226. C₂×#534	C₂×C₇	semidirect
227. C₂×#529	C₂×C₇	semidirect
228. C₂×#525	C₂×C₇	semidirect
229. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
230. C₂²×#121	C₂×C₇	semidirect
231. C₂×#518	C₂×C₇	semidirect
232. C₂²×C₄×D₄	C₂×C₇	semidirect
241. C₂⁴×C₇	#41	semidirect
349. C₂²×#41	C₂²×C₇	semidirect
350. C₂³×Q₈	C₂²×C₇	semidirect
353. C₂³×D₄	C₂²×C₇	semidirect
355. C₂⁴×C₄	C₂²×C₇	semidirect
356. #553	C₂²×C₇	semidirect
357. #553	C₂²×C₇	semidirect
358. #552	C₂²×C₇	semidirect
359. #551	C₂²×C₇	semidirect
360. #548	C₂²×C₇	semidirect
361. #546	C₂²×C₇	semidirect
362. #539	C₂²×C₇	semidirect
363. #538	C₂²×C₇	semidirect
364. #534	C₂²×C₇	semidirect
365. #529	C₂²×C₇	semidirect
366. C₂×#126	C₂²×C₇	semidirect
367. C₂×#126	C₂²×C₇	semidirect
368. C₂×#126	C₂²×C₇	semidirect
369. C₂×#125	C₂²×C₇	semidirect
370. C₂×#125	C₂²×C₇	semidirect
371. C₂×#124	C₂²×C₇	semidirect
372. C₂×#124	C₂²×C₇	semidirect
373. #525	C₂²×C₇	semidirect
375. C₂×#123	C₂²×C₇	semidirect
376. C₂×#123	C₂²×C₇	semidirect
377. C₂×#123	C₂²×C₇	semidirect
378. C₂×#123	C₂²×C₇	semidirect
379. C₂×C₂²⋊Q₈	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
384. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
385. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
388. C₂×#121	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
396. C₂×#120	C₂²×C₇	semidirect
397. #518	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
405. C₂×C₄×D₄	C₂²×C₇	semidirect
406. C₂×C₄×D₄	C₂²×C₇	semidirect
407. C₂×C₄×D₄	C₂²×C₇	semidirect
408. C₂×C₄×D₄	C₂²×C₇	semidirect
409. C₂×C₄×D₄	C₂²×C₇	semidirect
410. C₂×#117	C₂²×C₇	semidirect
411. C₂×#117	C₂²×C₇	semidirect
412. C₂×#117	C₂²×C₇	semidirect
413. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
414. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
415. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
416. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
419. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
420. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
421. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
422. C₂²×C₄²	C₂²×C₇	semidirect
449. C₂³×C₇	C₂×#41	semidirect
506. C₂×#41	C₂³×C₇	semidirect
510. C₂²×Q₈	C₂³×C₇	semidirect
524. C₂²×D₄	C₂³×C₇	semidirect
544. C₂³×C₄	C₂³×C₇	semidirect
545. #126	C₂³×C₇	semidirect
546. #126	C₂³×C₇	semidirect
547. #126	C₂³×C₇	semidirect
548. #125	C₂³×C₇	semidirect
549. #125	C₂³×C₇	semidirect
550. #124	C₂³×C₇	semidirect
551. #124	C₂³×C₇	semidirect
553. #123	C₂³×C₇	semidirect
554. #123	C₂³×C₇	semidirect
555. #123	C₂³×C₇	semidirect
556. #123	C₂³×C₇	semidirect
557. C₂²⋊Q₈	C₂³×C₇	semidirect
558. C₂²⋊Q₈	C₂³×C₇	semidirect
559. C₂²⋊Q₈	C₂³×C₇	semidirect
560. C₂²⋊Q₈	C₂³×C₇	semidirect
561. C₂²⋊Q₈	C₂³×C₇	semidirect
562. C₂²⋊Q₈	C₂³×C₇	semidirect
565. #121	C₂³×C₇	semidirect
566. #121	C₂³×C₇	semidirect
567. #121	C₂³×C₇	semidirect
568. #121	C₂³×C₇	semidirect
569. #121	C₂³×C₇	semidirect
570. #121	C₂³×C₇	semidirect
572. #120	C₂³×C₇	semidirect
573. C₄×Q₈	C₂³×C₇	semidirect
576. C₄×D₄	C₂³×C₇	semidirect
577. C₄×D₄	C₂³×C₇	semidirect
578. C₄×D₄	C₂³×C₇	semidirect
579. C₄×D₄	C₂³×C₇	semidirect
580. C₄×D₄	C₂³×C₇	semidirect
581. C₄×D₄	C₂³×C₇	semidirect
582. C₄×D₄	C₂³×C₇	semidirect
583. C₄×D₄	C₂³×C₇	semidirect
584. #117	C₂³×C₇	semidirect
585. #117	C₂³×C₇	semidirect
586. #117	C₂³×C₇	semidirect
599. C₂×C₄⋊C₄	C₂³×C₇	semidirect
600. C₂×C₄⋊C₄	C₂³×C₇	semidirect
601. C₂×C₄⋊C₄	C₂³×C₇	semidirect
602. C₂×C₄⋊C₄	C₂³×C₇	semidirect
619. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
620. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
621. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
626. C₂×C₄²	C₂³×C₇	semidirect
672. C₂⁴	C₇×#41	semidirect
785. C₂×C₇	#3505	direct (N × H)
815. C₂³	C₂×C₇×#41	semidirect
868. C₇	C₂×#3505	direct (N × H)
911. C₂	C₇×#3505	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×#3505	2
C₂×C₇×#553	2
C₂×C₇×#552	2
C₂×C₇×#551	2
C₂×C₇×#548	2
C₂×C₇×#546	2
C₂×C₇×#539	2
C₂×C₇×#538	2
C₂×C₇×#534	2
C₂×C₇×#529	2
C₂×C₇×#525	2
C₂²×C₇×C₂²⋊Q₈	2
C₂²×C₇×#121	2
C₂×C₇×#518	2
C₂²×C₄×C₇×D₄	2
C₂×#3505	7

Subgroups — C2×C7×#3505 #13239983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3505 #13239983