Subgroups — C₂×C₇×#3520 #13239988

Order 1792.

7910 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3520	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#554	C₂	1	2	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×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#548	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#546	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#542	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#539	C₂	1	4	yes	maximal, complemented
13	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
16	C₂²×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
17	C₂×C₇×#520	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₇×#41	C₂²	1	2	yes	—
20	C₂²×C₇×#41	C₂²	1	2	yes	complemented
21	C₂³×C₇×Q₈	C₂²	1	2	yes	complemented
22	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
24	C₇×#556	C₂²	1	16	yes	complemented
25	C₇×#554	C₂²	1	32	yes	complemented
26	C₇×#552	C₂²	1	32	yes	complemented
27	C₇×#551	C₂²	1	64	yes	complemented
28	C₇×D₄×Q₈	C₂²	1	16	yes	complemented
29	C₇×#548	C₂²	1	32	yes	complemented
30	C₇×#547	C₂²	1	16	yes	complemented
31	C₇×#547	C₂²	1	16	yes	complemented
32	C₇×#546	C₂²	1	32	yes	complemented
33	C₇×#542	C₂²	1	32	yes	complemented
34	C₇×#539	C₂²	1	64	yes	complemented
35	C₇×#533	C₂²	1	16	yes	complemented
36	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
39	C₇×#529	C₂²	1	16	yes	complemented
40	C₂×C₇×#126	C₂²	1	2	yes	complemented
41	C₂×C₇×#126	C₂²	1	4	yes	complemented
42	C₂×C₇×#126	C₂²	1	4	yes	complemented
43	C₂×C₇×#125	C₂²	1	1	yes	characteristic, 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, complemented
48	C₂×C₇×#124	C₂²	1	4	yes	complemented
49	C₇×#525	C₂²	1	32	yes	complemented
50	C₂×C₇×#123	C₂²	1	2	yes	—
51	C₂×C₇×#123	C₂²	1	4	yes	—
52	C₂×C₇×#123	C₂²	1	4	yes	complemented
53	C₂×C₇×#123	C₂²	1	4	yes	complemented
54	C₂×C₇×#123	C₂²	1	4	yes	complemented
55	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
56	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
64	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₂×C₇×C₂²⋊Q₈	C₂²	1	32	yes	complemented
67	C₂×C₇×#121	C₂²	1	1	yes	characteristic
68	C₂×C₇×#121	C₂²	1	4	yes	—
69	C₂×C₇×#121	C₂²	1	2	yes	—
70	C₂×C₇×#121	C₂²	1	2	yes	complemented
71	C₂×C₇×#120	C₂²	1	4	yes	—
72	C₇×#520	C₂²	1	32	yes	complemented
73	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
74	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
75	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
77	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
78	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
79	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
81	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
82	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
83	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
84	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
85	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
86	C₂×C₄×C₇×D₄	C₂²	1	16	yes	complemented
87	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
88	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
89	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₇×#117	C₂²	1	2	yes	—
91	C₂×C₇×#117	C₂²	1	2	yes	complemented
92	C₂×C₇×#117	C₂²	1	4	yes	complemented
93	C₂×C₇×#117	C₂²	1	2	yes	complemented
94	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	complemented
96	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
100	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
101	C₂×#3520	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁵×C₇	C₂³	1	2	yes	—
103	C₂×C₇×#41	—	2	16	no	—
104	C₂×C₇×#41	—	4	8	no	—
105	C₂×C₇×#41	C₂³	1	16	yes	—
106	C₂×C₇×#41	C₂³	1	16	yes	complemented
107	C₂²×C₇×Q₈	—	4	8	no	—
108	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×Q₈	C₂³	1	2	yes	—
110	C₂²×C₇×Q₈	C₂³	1	2	yes	—
111	C₂²×C₇×Q₈	C₂³	1	4	yes	—
112	C₂²×C₇×Q₈	C₂³	1	16	yes	complemented
113	C₂²×C₇×D₄	—	2	8	no	—
114	C₂²×C₇×D₄	C₂³	1	2	yes	—
115	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₇×D₄	C₂³	1	8	yes	—
117	C₂²×C₇×D₄	C₂³	1	4	yes	—
118	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
119	C₂²×C₇×D₄	C₂³	1	2	yes	—
120	C₂²×C₇×D₄	C₂³	1	4	yes	—
121	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇	—	4	8	no	—
123	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	2	yes	—
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	4	yes	—
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	16	yes	—
136	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
137	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
138	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
139	C₇×#126	C₂³	1	16	yes	complemented
140	C₇×#126	C₂³	1	32	yes	complemented
141	C₇×#126	C₂³	1	32	yes	complemented
142	C₇×#125	C₂³	1	8	yes	complemented
143	C₇×#125	C₂³	1	16	yes	complemented
144	C₇×#125	C₂³	1	32	yes	complemented
145	C₇×#124	C₂³	1	16	yes	—
146	C₇×#124	C₂³	1	8	yes	complemented
147	C₇×#124	C₂³	1	32	yes	complemented
148	C₇×#123	C₂³	1	16	yes	—
149	C₇×#123	C₂³	1	32	yes	—
150	C₇×#123	C₂³	1	32	yes	complemented
151	C₇×#123	C₂³	1	32	yes	complemented
152	C₇×#123	C₂³	1	32	yes	complemented
153	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
154	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
155	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
156	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
157	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
158	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
159	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
160	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
161	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
162	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
163	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
164	C₇×#121	C₂³	1	8	yes	—
165	C₇×#121	C₂³	1	32	yes	—
166	C₇×#121	C₂³	1	16	yes	—
167	C₇×#121	C₂³	1	16	yes	complemented
168	C₇×#120	C₂³	1	32	yes	—
169	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
170	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
171	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
172	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
173	C₄×C₇×D₄	C₂³	1	8	yes	—
174	C₄×C₇×D₄	C₂³	1	16	yes	—
175	C₄×C₇×D₄	C₂³	1	8	yes	—
176	C₄×C₇×D₄	C₂³	1	8	yes	—
177	C₄×C₇×D₄	C₂³	1	8	yes	—
178	C₄×C₇×D₄	C₂³	1	16	yes	—
179	C₄×C₇×D₄	C₂³	1	16	yes	—
180	C₄×C₇×D₄	C₂³	1	32	yes	—
181	C₄×C₇×D₄	C₂³	1	16	yes	—
182	C₄×C₇×D₄	C₂³	1	32	yes	complemented
183	C₄×C₇×D₄	C₂³	1	32	yes	complemented
184	C₄×C₇×D₄	C₂³	1	8	yes	complemented
185	C₇×#117	C₂³	1	16	yes	—
186	C₇×#117	C₂³	1	16	yes	complemented
187	C₇×#117	C₂³	1	32	yes	complemented
188	C₇×#117	C₂³	1	16	yes	complemented
189	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
200	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
206	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	complemented
210	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
211	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
212	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
214	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	—
222	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
226	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
228	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	8	yes	—
234	C₂×C₄²×C₇	C₂³	1	4	yes	—
235	C₂×C₄²×C₇	C₂³	1	4	yes	—
236	C₂×C₄²×C₇	C₂³	1	2	yes	—
237	#3520	C₂×C₇	1	32	yes	direct product factor
238	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
239	C₂×#554	C₂×C₇	1	2	yes	complemented
240	C₂×#552	C₂×C₇	1	2	yes	complemented
241	C₂×#551	C₂×C₇	1	4	yes	complemented
242	C₂×D₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
243	C₂×#548	C₂×C₇	1	2	yes	complemented
244	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
245	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
246	C₂×#546	C₂×C₇	1	2	yes	complemented
247	C₂×#542	C₂×C₇	1	2	yes	complemented
248	C₂×#539	C₂×C₇	1	4	yes	complemented
249	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
250	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
251	C₂×#525	C₂×C₇	1	2	yes	complemented
252	C₂²×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
253	C₂×#520	C₂×C₇	1	2	yes	complemented
254	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
255	C₂⁴×C₇	—	2	8	no	—
256	C₂⁴×C₇	—	2	8	no	—
257	C₂⁴×C₇	—	4	4	no	—
258	C₂⁴×C₇	C₂⁴	1	2	yes	—
259	C₂⁴×C₇	C₂⁴	1	2	yes	—
260	C₂⁴×C₇	C₂⁴	1	8	yes	—
261	C₂⁴×C₇	C₂⁴	1	2	yes	—
262	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
263	C₇×#41	—	2	64	no	—
264	C₇×#41	—	4	32	no	—
265	C₂×C₇×Q₈	—	2	8	no	—
266	C₂×C₇×Q₈	—	2	4	no	—
267	C₂×C₇×Q₈	—	2	8	no	—
268	C₂×C₇×Q₈	—	4	8	no	—
269	C₂×C₇×Q₈	—	4	32	no	—
270	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
271	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
272	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
273	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
274	C₂×C₇×D₄	—	2	8	no	—
275	C₂×C₇×D₄	—	2	16	no	—
276	C₂×C₇×D₄	—	2	8	no	—
277	C₂×C₇×D₄	—	2	32	no	—
278	C₂×C₇×D₄	—	2	4	no	—
279	C₂×C₇×D₄	—	2	4	no	—
280	C₂×C₇×D₄	—	4	8	no	—
281	C₂×C₇×D₄	#41	1	8	yes	complemented
282	C₂×C₇×D₄	C₂⁴	1	8	yes	—
283	C₂×C₇×D₄	C₂⁴	1	8	yes	—
284	C₂×C₇×D₄	C₂⁴	1	4	yes	—
285	C₂×C₇×D₄	C₂⁴	1	16	yes	—
286	C₂×C₇×D₄	C₂⁴	1	4	yes	—
287	C₂×C₇×D₄	C₂⁴	1	16	yes	—
288	C₂×C₇×D₄	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₇	—	2	16	no	—
290	C₂²×C₄×C₇	—	2	4	no	—
291	C₂²×C₄×C₇	—	2	4	no	—
292	C₂²×C₄×C₇	—	2	8	no	—
293	C₂²×C₄×C₇	—	2	4	no	—
294	C₂²×C₄×C₇	—	2	8	no	—
295	C₂²×C₄×C₇	—	2	8	no	—
296	C₂²×C₄×C₇	—	4	32	no	—
297	C₂²×C₄×C₇	—	4	4	no	—
298	C₂²×C₄×C₇	—	4	4	no	—
299	C₂²×C₄×C₇	—	4	4	no	—
300	C₂²×C₄×C₇	—	4	8	no	—
301	C₂²×C₄×C₇	—	4	8	no	—
302	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
321	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
322	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
325	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
327	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
330	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
331	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
332	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
333	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
334	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
335	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
336	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
337	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
338	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
339	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
340	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
341	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
342	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
343	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
344	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
345	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
346	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
347	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
348	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
349	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
350	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
351	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
352	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
353	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
354	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
355	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
356	C₇×C₂²⋊C₄	C₂⁴	1	8	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	C₄²×C₇	C₂⁴	1	4	yes	—
362	C₄²×C₇	C₂⁴	1	4	yes	—
363	C₄²×C₇	C₂⁴	1	4	yes	—
364	C₄²×C₇	C₂⁴	1	4	yes	—
365	C₄²×C₇	C₂⁴	1	16	yes	—
366	C₄²×C₇	C₂⁴	1	16	yes	—
367	C₄²×C₇	C₂⁴	1	8	yes	—
368	C₂²×#41	C₂²×C₇	1	2	yes	—
369	C₂²×#41	C₂²×C₇	1	2	yes	complemented
370	C₂³×Q₈	C₂²×C₇	1	2	yes	complemented
371	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
372	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
373	#556	C₂²×C₇	1	16	yes	complemented
374	#554	C₂²×C₇	1	32	yes	complemented
375	#552	C₂²×C₇	1	32	yes	complemented
376	#551	C₂²×C₇	1	64	yes	complemented
377	D₄×Q₈	C₂²×C₇	1	16	yes	complemented
378	#548	C₂²×C₇	1	32	yes	complemented
379	#547	C₂²×C₇	1	16	yes	complemented
380	#547	C₂²×C₇	1	16	yes	complemented
381	#546	C₂²×C₇	1	32	yes	complemented
382	#542	C₂²×C₇	1	32	yes	complemented
383	#539	C₂²×C₇	1	64	yes	complemented
384	#533	C₂²×C₇	1	16	yes	complemented
385	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
386	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
387	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
388	#529	C₂²×C₇	1	16	yes	complemented
389	C₂×#126	C₂²×C₇	1	2	yes	complemented
390	C₂×#126	C₂²×C₇	1	4	yes	complemented
391	C₂×#126	C₂²×C₇	1	4	yes	complemented
392	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
393	C₂×#125	C₂²×C₇	1	2	yes	complemented
394	C₂×#125	C₂²×C₇	1	4	yes	complemented
395	C₂×#124	C₂²×C₇	1	2	yes	—
396	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
397	C₂×#124	C₂²×C₇	1	4	yes	complemented
398	#525	C₂²×C₇	1	32	yes	complemented
399	C₂×#123	C₂²×C₇	1	2	yes	—
400	C₂×#123	C₂²×C₇	1	4	yes	—
401	C₂×#123	C₂²×C₇	1	4	yes	complemented
402	C₂×#123	C₂²×C₇	1	4	yes	complemented
403	C₂×#123	C₂²×C₇	1	4	yes	complemented
404	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
406	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
407	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
408	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
409	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
410	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
411	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
412	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
413	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
414	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
415	C₂×C₂²⋊Q₈	C₂²×C₇	1	32	yes	complemented
416	C₂×#121	C₂²×C₇	1	1	yes	characteristic
417	C₂×#121	C₂²×C₇	1	4	yes	—
418	C₂×#121	C₂²×C₇	1	2	yes	—
419	C₂×#121	C₂²×C₇	1	2	yes	complemented
420	C₂×#120	C₂²×C₇	1	4	yes	—
421	#520	C₂²×C₇	1	32	yes	complemented
422	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
423	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
424	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
425	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
426	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
432	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
433	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
434	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
435	C₂×C₄×D₄	C₂²×C₇	1	16	yes	complemented
436	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
437	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
438	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
439	C₂×#117	C₂²×C₇	1	2	yes	—
440	C₂×#117	C₂²×C₇	1	2	yes	complemented
441	C₂×#117	C₂²×C₇	1	4	yes	complemented
442	C₂×#117	C₂²×C₇	1	2	yes	complemented
443	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	complemented
445	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
446	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
447	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
448	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
449	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
450	C₂³×C₇	—	2	2	no	—
451	C₂³×C₇	—	2	4	no	—
452	C₂³×C₇	—	2	2	no	—
453	C₂³×C₇	—	2	4	no	—
454	C₂³×C₇	—	2	4	no	—
455	C₂³×C₇	—	2	16	no	—
456	C₂³×C₇	—	2	4	no	—
457	C₂³×C₇	—	2	4	no	—
458	C₂³×C₇	—	2	4	no	—
459	C₂³×C₇	—	2	4	no	—
460	C₂³×C₇	—	2	16	no	—
461	C₂³×C₇	—	2	4	no	—
462	C₂³×C₇	—	4	8	no	—
463	C₂³×C₇	—	4	32	no	—
464	C₂³×C₇	C₂×#41	1	8	yes	—
465	C₂³×C₇	2₋¹⁺⁴	1	4	yes	—
466	C₂³×C₇	C₂⁵	1	4	yes	—
467	C₂³×C₇	C₂⁵	1	4	yes	—
468	C₂³×C₇	C₂⁵	1	4	yes	—
469	C₂³×C₇	C₂⁵	1	2	yes	—
470	C₂³×C₇	C₂⁵	1	1	yes	characteristic
471	C₇×Q₈	—	2	16	no	—
472	C₇×Q₈	—	2	8	no	—
473	C₇×Q₈	—	2	16	no	—
474	C₇×Q₈	—	4	16	no	—
475	C₇×D₄	—	2	16	no	—
476	C₇×D₄	—	2	32	no	—
477	C₇×D₄	—	2	16	no	—
478	C₇×D₄	—	2	8	no	—
479	C₇×D₄	—	2	8	no	—
480	C₇×D₄	—	4	16	no	—
481	C₇×D₄	C₂×#41	1	16	yes	complemented
482	C₂×C₄×C₇	—	2	4	no	—
483	C₂×C₄×C₇	—	2	2	no	—
484	C₂×C₄×C₇	—	2	8	no	—
485	C₂×C₄×C₇	—	2	32	no	—
486	C₂×C₄×C₇	—	2	2	no	—
487	C₂×C₄×C₇	—	2	4	no	—
488	C₂×C₄×C₇	—	2	4	no	—
489	C₂×C₄×C₇	—	2	8	no	—
490	C₂×C₄×C₇	—	2	4	no	—
491	C₂×C₄×C₇	—	2	8	no	—
492	C₂×C₄×C₇	—	2	2	no	—
493	C₂×C₄×C₇	—	2	2	no	—
494	C₂×C₄×C₇	—	2	4	no	—
495	C₂×C₄×C₇	—	2	8	no	—
496	C₂×C₄×C₇	—	2	16	no	—
497	C₂×C₄×C₇	—	2	8	no	—
498	C₂×C₄×C₇	—	2	16	no	—
499	C₂×C₄×C₇	—	2	16	no	—
500	C₂×C₄×C₇	—	4	8	no	—
501	C₂×C₄×C₇	—	4	8	no	—
502	C₂×C₄×C₇	—	4	8	no	—
503	C₂×C₄×C₇	—	4	16	no	—
504	C₂×C₄×C₇	—	4	16	no	—
505	C₂×C₄×C₇	C₂×#41	1	4	yes	—
506	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
507	C₂×C₄×C₇	C₂⁵	1	2	yes	—
508	C₂×C₄×C₇	C₂⁵	1	4	yes	—
509	C₂×C₄×C₇	C₂⁵	1	2	yes	—
510	C₂×C₄×C₇	C₂⁵	1	8	yes	—
511	C₂×C₄×C₇	C₂⁵	1	2	yes	—
512	C₂×C₄×C₇	C₂⁵	1	2	yes	—
513	C₂×C₄×C₇	C₂⁵	1	4	yes	—
514	C₂×C₄×C₇	C₂⁵	1	4	yes	—
515	C₂×C₄×C₇	C₂⁵	1	8	yes	—
516	C₂×C₄×C₇	C₂⁵	1	4	yes	—
517	C₂×C₄×C₇	C₂⁵	1	4	yes	—
518	C₂×C₄×C₇	C₂⁵	1	2	yes	—
519	C₂×C₄×C₇	C₂⁵	1	2	yes	—
520	C₂⁵	C₂³×C₇	1	2	yes	—
521	C₂×#41	—	2	16	no	—
522	C₂×#41	—	4	8	no	—
523	C₂×#41	C₂³×C₇	1	16	yes	—
524	C₂×#41	C₂³×C₇	1	16	yes	complemented
525	C₂²×Q₈	—	4	8	no	—
526	C₂²×Q₈	C₂³×C₇	1	2	yes	—
527	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
528	C₂²×Q₈	C₂³×C₇	1	2	yes	—
529	C₂²×Q₈	C₂³×C₇	1	4	yes	—
530	C₂²×Q₈	C₂³×C₇	1	16	yes	complemented
531	C₂²×D₄	—	2	8	no	—
532	C₂²×D₄	C₂³×C₇	1	2	yes	—
533	C₂²×D₄	C₂³×C₇	1	2	yes	—
534	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₇	1	4	yes	—
536	C₂²×D₄	C₂³×C₇	1	8	yes	—
537	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₇	1	4	yes	—
539	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
540	C₂³×C₄	—	4	8	no	—
541	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₇	1	4	yes	—
543	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₇	1	2	yes	—
545	C₂³×C₄	C₂³×C₇	1	2	yes	—
546	C₂³×C₄	C₂³×C₇	1	2	yes	—
547	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₇	1	2	yes	—
549	C₂³×C₄	C₂³×C₇	1	4	yes	—
550	C₂³×C₄	C₂³×C₇	1	2	yes	—
551	C₂³×C₄	C₂³×C₇	1	4	yes	—
552	C₂³×C₄	C₂³×C₇	1	2	yes	—
553	C₂³×C₄	C₂³×C₇	1	16	yes	—
554	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
555	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
556	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
557	#126	C₂³×C₇	1	16	yes	complemented
558	#126	C₂³×C₇	1	32	yes	complemented
559	#126	C₂³×C₇	1	32	yes	complemented
560	#125	C₂³×C₇	1	8	yes	complemented
561	#125	C₂³×C₇	1	16	yes	complemented
562	#125	C₂³×C₇	1	32	yes	complemented
563	#124	C₂³×C₇	1	16	yes	—
564	#124	C₂³×C₇	1	8	yes	complemented
565	#124	C₂³×C₇	1	32	yes	complemented
566	#123	C₂³×C₇	1	16	yes	—
567	#123	C₂³×C₇	1	32	yes	—
568	#123	C₂³×C₇	1	32	yes	complemented
569	#123	C₂³×C₇	1	32	yes	complemented
570	#123	C₂³×C₇	1	32	yes	complemented
571	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
572	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
573	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
574	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
575	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
576	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
577	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
578	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
579	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
580	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
581	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
582	#121	C₂³×C₇	1	8	yes	—
583	#121	C₂³×C₇	1	32	yes	—
584	#121	C₂³×C₇	1	16	yes	—
585	#121	C₂³×C₇	1	16	yes	complemented
586	#120	C₂³×C₇	1	32	yes	—
587	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
588	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
589	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
590	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
591	C₄×D₄	C₂³×C₇	1	8	yes	—
592	C₄×D₄	C₂³×C₇	1	16	yes	—
593	C₄×D₄	C₂³×C₇	1	8	yes	—
594	C₄×D₄	C₂³×C₇	1	8	yes	—
595	C₄×D₄	C₂³×C₇	1	8	yes	—
596	C₄×D₄	C₂³×C₇	1	16	yes	—
597	C₄×D₄	C₂³×C₇	1	16	yes	—
598	C₄×D₄	C₂³×C₇	1	32	yes	—
599	C₄×D₄	C₂³×C₇	1	16	yes	—
600	C₄×D₄	C₂³×C₇	1	32	yes	complemented
601	C₄×D₄	C₂³×C₇	1	32	yes	complemented
602	C₄×D₄	C₂³×C₇	1	8	yes	complemented
603	#117	C₂³×C₇	1	16	yes	—
604	#117	C₂³×C₇	1	16	yes	complemented
605	#117	C₂³×C₇	1	32	yes	complemented
606	#117	C₂³×C₇	1	16	yes	complemented
607	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
613	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
617	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
624	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	complemented
628	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
629	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
630	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₇	1	4	yes	—
648	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₇	1	4	yes	—
650	C₂×C₄²	C₂³×C₇	1	2	yes	—
651	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₇	1	8	yes	—
655	C₂²×C₇	—	2	2	no	—
656	C₂²×C₇	—	2	4	no	—
657	C₂²×C₇	—	2	2	no	—
658	C₂²×C₇	—	2	4	no	—
659	C₂²×C₇	—	2	8	no	—
660	C₂²×C₇	—	2	16	no	—
661	C₂²×C₇	—	2	4	no	—
662	C₂²×C₇	—	2	4	no	—
663	C₂²×C₇	—	2	4	no	—
664	C₂²×C₇	—	2	4	no	—
665	C₂²×C₇	—	2	4	no	—
666	C₂²×C₇	—	2	4	no	—
667	C₂²×C₇	—	4	32	no	—
668	C₂²×C₇	—	4	8	no	—
669	C₂²×C₇	—	4	8	no	—
670	C₂²×C₇	C₂²×#41	1	8	yes	—
671	C₂²×C₇	C₂²×#41	1	2	yes	—
672	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
673	C₂²×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
674	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
675	C₂²×C₇	C₂⁶	1	1	yes	characteristic
676	C₄×C₇	—	2	4	no	—
677	C₄×C₇	—	2	2	no	—
678	C₄×C₇	—	2	8	no	—
679	C₄×C₇	—	2	2	no	—
680	C₄×C₇	—	2	4	no	—
681	C₄×C₇	—	2	4	no	—
682	C₄×C₇	—	2	8	no	—
683	C₄×C₇	—	2	4	no	—
684	C₄×C₇	—	2	2	no	—
685	C₄×C₇	—	2	2	no	—
686	C₄×C₇	—	2	4	no	—
687	C₄×C₇	C₂²×#41	1	4	yes	—
688	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
689	C₂⁴	—	2	8	no	—
690	C₂⁴	—	2	8	no	—
691	C₂⁴	—	4	4	no	—
692	C₂⁴	C₂⁴×C₇	1	2	yes	—
693	C₂⁴	C₂⁴×C₇	1	2	yes	—
694	C₂⁴	C₂⁴×C₇	1	8	yes	—
695	C₂⁴	C₂⁴×C₇	1	2	yes	—
696	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
697	#41	—	2	64	no	—
698	#41	—	4	32	no	—
699	C₂×Q₈	—	2	8	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	2	8	no	—
702	C₂×Q₈	—	4	8	no	—
703	C₂×Q₈	—	4	32	no	—
704	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
705	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
706	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
707	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
708	C₂×D₄	—	2	8	no	—
709	C₂×D₄	—	2	16	no	—
710	C₂×D₄	—	2	8	no	—
711	C₂×D₄	—	2	32	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	4	8	no	—
715	C₂×D₄	C₇×#41	1	8	yes	complemented
716	C₂×D₄	C₂⁴×C₇	1	8	yes	—
717	C₂×D₄	C₂⁴×C₇	1	8	yes	—
718	C₂×D₄	C₂⁴×C₇	1	4	yes	—
719	C₂×D₄	C₂⁴×C₇	1	16	yes	—
720	C₂×D₄	C₂⁴×C₇	1	4	yes	—
721	C₂×D₄	C₂⁴×C₇	1	16	yes	—
722	C₂×D₄	C₂⁴×C₇	1	4	yes	—
723	C₂²×C₄	—	2	16	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	8	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	8	no	—
729	C₂²×C₄	—	2	8	no	—
730	C₂²×C₄	—	4	32	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	—	4	4	no	—
733	C₂²×C₄	—	4	4	no	—
734	C₂²×C₄	—	4	8	no	—
735	C₂²×C₄	—	4	8	no	—
736	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
741	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
745	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
746	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
751	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
752	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
753	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
754	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
755	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
756	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
757	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
758	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
759	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
761	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
762	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
763	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
764	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
765	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
766	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
767	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
770	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
771	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
772	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
773	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
774	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
775	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
776	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
777	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
779	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
780	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
781	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
782	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
784	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
785	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
786	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
787	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
788	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
789	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
790	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
791	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
792	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
794	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
795	C₄²	C₂⁴×C₇	1	4	yes	—
796	C₄²	C₂⁴×C₇	1	4	yes	—
797	C₄²	C₂⁴×C₇	1	4	yes	—
798	C₄²	C₂⁴×C₇	1	4	yes	—
799	C₄²	C₂⁴×C₇	1	16	yes	—
800	C₄²	C₂⁴×C₇	1	16	yes	—
801	C₄²	C₂⁴×C₇	1	8	yes	—
802	C₂×C₇	—	2	4	no	—
803	C₂×C₇	—	2	8	no	—
804	C₂×C₇	—	4	4	no	—
805	C₂×C₇	—	4	4	no	—
806	C₂×C₇	#3520	1	4	yes	direct product factor
807	C₂×C₇	C₂³×#41	1	1	yes	characteristic
808	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
809	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
810	C₂³	—	2	2	no	—
811	C₂³	—	2	4	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	16	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	4	no	—
819	C₂³	—	2	4	no	—
820	C₂³	—	2	16	no	—
821	C₂³	—	2	4	no	—
822	C₂³	—	4	8	no	—
823	C₂³	—	4	32	no	—
824	C₂³	C₂×C₇×#41	1	8	yes	—
825	C₂³	C₇×2₋¹⁺⁴	1	4	yes	—
826	C₂³	C₂⁵×C₇	1	4	yes	—
827	C₂³	C₂⁵×C₇	1	4	yes	—
828	C₂³	C₂⁵×C₇	1	4	yes	—
829	C₂³	C₂⁵×C₇	1	2	yes	—
830	C₂³	C₂⁵×C₇	1	1	yes	characteristic
831	Q₈	—	2	16	no	—
832	Q₈	—	2	8	no	—
833	Q₈	—	2	16	no	—
834	Q₈	—	4	16	no	—
835	D₄	—	2	16	no	—
836	D₄	—	2	32	no	—
837	D₄	—	2	16	no	—
838	D₄	—	2	8	no	—
839	D₄	—	2	8	no	—
840	D₄	—	4	16	no	—
841	D₄	C₂×C₇×#41	1	16	yes	complemented
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	8	no	—
845	C₂×C₄	—	2	32	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	8	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	8	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	16	no	—
857	C₂×C₄	—	2	8	no	—
858	C₂×C₄	—	2	16	no	—
859	C₂×C₄	—	2	16	no	—
860	C₂×C₄	—	4	8	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	16	no	—
864	C₂×C₄	—	4	16	no	—
865	C₂×C₄	C₂×C₇×#41	1	4	yes	—
866	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
867	C₂×C₄	C₂⁵×C₇	1	2	yes	—
868	C₂×C₄	C₂⁵×C₇	1	4	yes	—
869	C₂×C₄	C₂⁵×C₇	1	2	yes	—
870	C₂×C₄	C₂⁵×C₇	1	8	yes	—
871	C₂×C₄	C₂⁵×C₇	1	2	yes	—
872	C₂×C₄	C₂⁵×C₇	1	2	yes	—
873	C₂×C₄	C₂⁵×C₇	1	4	yes	—
874	C₂×C₄	C₂⁵×C₇	1	4	yes	—
875	C₂×C₄	C₂⁵×C₇	1	8	yes	—
876	C₂×C₄	C₂⁵×C₇	1	4	yes	—
877	C₂×C₄	C₂⁵×C₇	1	4	yes	—
878	C₂×C₄	C₂⁵×C₇	1	2	yes	—
879	C₂×C₄	C₂⁵×C₇	1	2	yes	—
880	C₇	C₂×#3520	1	1	yes	characteristic, direct product factor, Sylow
881	C₂²	—	2	2	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	8	no	—
886	C₂²	—	2	16	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	4	32	no	—
894	C₂²	—	4	8	no	—
895	C₂²	—	4	8	no	—
896	C₂²	C₂²×C₇×#41	1	8	yes	—
897	C₂²	C₂²×C₇×#41	1	2	yes	—
898	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
899	C₂²	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
900	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
901	C₂²	C₂⁶×C₇	1	1	yes	characteristic
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	8	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	4	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	8	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	4	no	—
913	C₄	C₂²×C₇×#41	1	4	yes	—
914	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
915	C₂	—	2	4	no	—
916	C₂	—	2	8	no	—
917	C₂	—	4	4	no	—
918	C₂	—	4	4	no	—
919	C₂	C₇×#3520	1	4	yes	direct product factor
920	C₂	C₂³×C₇×#41	1	1	yes	characteristic
921	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
922	C₂	C₂²×C₇×2₋¹⁺⁴	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×#3520	C₂	direct (N × H)
2. C₂×C₇×#556	C₂	semidirect
3. C₂×C₇×#554	C₂	semidirect
4. C₂×C₇×#552	C₂	semidirect
5. C₂×C₇×#551	C₂	semidirect
6. C₂×C₇×D₄×Q₈	C₂	semidirect
7. C₂×C₇×#548	C₂	semidirect
8. C₂×C₇×#547	C₂	semidirect
9. C₂×C₇×#547	C₂	semidirect
10. C₂×C₇×#546	C₂	semidirect
11. C₂×C₇×#542	C₂	semidirect
12. C₂×C₇×#539	C₂	semidirect
13. C₂×C₇×#533	C₂	semidirect
14. C₂×C₇×#529	C₂	semidirect
15. C₂×C₇×#525	C₂	semidirect
16. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
17. C₂×C₇×#520	C₂	semidirect
18. C₂²×C₄×C₇×D₄	C₂	semidirect
20. C₂²×C₇×#41	C₂²	semidirect
21. C₂³×C₇×Q₈	C₂²	semidirect
24. C₇×#556	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
26. C₇×#552	C₂²	semidirect
27. C₇×#551	C₂²	semidirect
28. C₇×D₄×Q₈	C₂²	semidirect
29. C₇×#548	C₂²	semidirect
30. C₇×#547	C₂²	semidirect
31. C₇×#547	C₂²	semidirect
32. C₇×#546	C₂²	semidirect
33. C₇×#542	C₂²	semidirect
34. C₇×#539	C₂²	semidirect
35. C₇×#533	C₂²	semidirect
36. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
39. C₇×#529	C₂²	semidirect
40. C₂×C₇×#126	C₂²	semidirect
41. C₂×C₇×#126	C₂²	semidirect
42. C₂×C₇×#126	C₂²	semidirect
43. C₂×C₇×#125	C₂²	semidirect
44. C₂×C₇×#125	C₂²	semidirect
45. C₂×C₇×#125	C₂²	semidirect
47. C₂×C₇×#124	C₂²	semidirect
48. C₂×C₇×#124	C₂²	semidirect
49. C₇×#525	C₂²	semidirect
52. C₂×C₇×#123	C₂²	semidirect
53. C₂×C₇×#123	C₂²	semidirect
54. 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
63. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
65. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
66. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
70. C₂×C₇×#121	C₂²	semidirect
72. C₇×#520	C₂²	semidirect
73. C₂×C₄×C₇×Q₈	C₂²	semidirect
74. C₂×C₄×C₇×Q₈	C₂²	semidirect
75. C₂×C₄×C₇×Q₈	C₂²	semidirect
76. C₂×C₄×C₇×Q₈	C₂²	semidirect
86. C₂×C₄×C₇×D₄	C₂²	semidirect
87. C₂×C₄×C₇×D₄	C₂²	semidirect
88. C₂×C₄×C₇×D₄	C₂²	semidirect
89. C₂×C₄×C₇×D₄	C₂²	semidirect
91. C₂×C₇×#117	C₂²	semidirect
92. C₂×C₇×#117	C₂²	semidirect
93. C₂×C₇×#117	C₂²	semidirect
95. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
96. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
97. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
101. C₂×#3520	C₇	direct (N × H)
106. C₂×C₇×#41	C₂³	semidirect
112. C₂²×C₇×Q₈	C₂³	semidirect
136. C₇×C₄⋊Q₈	C₂³	semidirect
137. C₇×C₄⋊Q₈	C₂³	semidirect
138. C₇×C₄⋊Q₈	C₂³	semidirect
139. C₇×#126	C₂³	semidirect
140. C₇×#126	C₂³	semidirect
141. C₇×#126	C₂³	semidirect
142. C₇×#125	C₂³	semidirect
143. C₇×#125	C₂³	semidirect
144. C₇×#125	C₂³	semidirect
146. C₇×#124	C₂³	semidirect
147. C₇×#124	C₂³	semidirect
150. C₇×#123	C₂³	semidirect
151. C₇×#123	C₂³	semidirect
152. C₇×#123	C₂³	semidirect
157. C₇×C₂²⋊Q₈	C₂³	semidirect
158. C₇×C₂²⋊Q₈	C₂³	semidirect
159. C₇×C₂²⋊Q₈	C₂³	semidirect
160. C₇×C₂²⋊Q₈	C₂³	semidirect
161. C₇×C₂²⋊Q₈	C₂³	semidirect
162. C₇×C₂²⋊Q₈	C₂³	semidirect
163. C₇×C₂²⋊Q₈	C₂³	semidirect
167. C₇×#121	C₂³	semidirect
169. C₄×C₇×Q₈	C₂³	semidirect
170. C₄×C₇×Q₈	C₂³	semidirect
171. C₄×C₇×Q₈	C₂³	semidirect
172. C₄×C₇×Q₈	C₂³	semidirect
182. C₄×C₇×D₄	C₂³	semidirect
183. C₄×C₇×D₄	C₂³	semidirect
184. C₄×C₇×D₄	C₂³	semidirect
186. C₇×#117	C₂³	semidirect
187. C₇×#117	C₂³	semidirect
188. C₇×#117	C₂³	semidirect
209. C₂×C₇×C₄⋊C₄	C₂³	semidirect
210. C₂×C₇×C₄⋊C₄	C₂³	semidirect
211. C₂×C₇×C₄⋊C₄	C₂³	semidirect
237. #3520	C₂×C₇	direct (N × H)
238. C₂×#556	C₂×C₇	semidirect
239. C₂×#554	C₂×C₇	semidirect
240. C₂×#552	C₂×C₇	semidirect
241. C₂×#551	C₂×C₇	semidirect
242. C₂×D₄×Q₈	C₂×C₇	semidirect
243. C₂×#548	C₂×C₇	semidirect
244. C₂×#547	C₂×C₇	semidirect
245. C₂×#547	C₂×C₇	semidirect
246. C₂×#546	C₂×C₇	semidirect
247. C₂×#542	C₂×C₇	semidirect
248. C₂×#539	C₂×C₇	semidirect
249. C₂×#533	C₂×C₇	semidirect
250. C₂×#529	C₂×C₇	semidirect
251. C₂×#525	C₂×C₇	semidirect
252. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
253. C₂×#520	C₂×C₇	semidirect
254. C₂²×C₄×D₄	C₂×C₇	semidirect
281. C₂×C₇×D₄	#41	semidirect
369. C₂²×#41	C₂²×C₇	semidirect
370. C₂³×Q₈	C₂²×C₇	semidirect
373. #556	C₂²×C₇	semidirect
374. #554	C₂²×C₇	semidirect
375. #552	C₂²×C₇	semidirect
376. #551	C₂²×C₇	semidirect
377. D₄×Q₈	C₂²×C₇	semidirect
378. #548	C₂²×C₇	semidirect
379. #547	C₂²×C₇	semidirect
380. #547	C₂²×C₇	semidirect
381. #546	C₂²×C₇	semidirect
382. #542	C₂²×C₇	semidirect
383. #539	C₂²×C₇	semidirect
384. #533	C₂²×C₇	semidirect
385. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
386. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
387. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
388. #529	C₂²×C₇	semidirect
389. C₂×#126	C₂²×C₇	semidirect
390. C₂×#126	C₂²×C₇	semidirect
391. C₂×#126	C₂²×C₇	semidirect
392. C₂×#125	C₂²×C₇	semidirect
393. C₂×#125	C₂²×C₇	semidirect
394. C₂×#125	C₂²×C₇	semidirect
396. C₂×#124	C₂²×C₇	semidirect
397. C₂×#124	C₂²×C₇	semidirect
398. #525	C₂²×C₇	semidirect
401. C₂×#123	C₂²×C₇	semidirect
402. C₂×#123	C₂²×C₇	semidirect
403. C₂×#123	C₂²×C₇	semidirect
408. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
409. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
410. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
411. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
412. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
413. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
414. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
415. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
419. C₂×#121	C₂²×C₇	semidirect
421. #520	C₂²×C₇	semidirect
422. C₂×C₄×Q₈	C₂²×C₇	semidirect
423. C₂×C₄×Q₈	C₂²×C₇	semidirect
424. C₂×C₄×Q₈	C₂²×C₇	semidirect
425. C₂×C₄×Q₈	C₂²×C₇	semidirect
435. C₂×C₄×D₄	C₂²×C₇	semidirect
436. C₂×C₄×D₄	C₂²×C₇	semidirect
437. C₂×C₄×D₄	C₂²×C₇	semidirect
438. C₂×C₄×D₄	C₂²×C₇	semidirect
440. C₂×#117	C₂²×C₇	semidirect
441. C₂×#117	C₂²×C₇	semidirect
442. C₂×#117	C₂²×C₇	semidirect
444. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
445. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
446. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
481. C₇×D₄	C₂×#41	semidirect
524. C₂×#41	C₂³×C₇	semidirect
530. C₂²×Q₈	C₂³×C₇	semidirect
554. C₄⋊Q₈	C₂³×C₇	semidirect
555. C₄⋊Q₈	C₂³×C₇	semidirect
556. C₄⋊Q₈	C₂³×C₇	semidirect
557. #126	C₂³×C₇	semidirect
558. #126	C₂³×C₇	semidirect
559. #126	C₂³×C₇	semidirect
560. #125	C₂³×C₇	semidirect
561. #125	C₂³×C₇	semidirect
562. #125	C₂³×C₇	semidirect
564. #124	C₂³×C₇	semidirect
565. #124	C₂³×C₇	semidirect
568. #123	C₂³×C₇	semidirect
569. #123	C₂³×C₇	semidirect
570. #123	C₂³×C₇	semidirect
575. C₂²⋊Q₈	C₂³×C₇	semidirect
576. C₂²⋊Q₈	C₂³×C₇	semidirect
577. C₂²⋊Q₈	C₂³×C₇	semidirect
578. C₂²⋊Q₈	C₂³×C₇	semidirect
579. C₂²⋊Q₈	C₂³×C₇	semidirect
580. C₂²⋊Q₈	C₂³×C₇	semidirect
581. C₂²⋊Q₈	C₂³×C₇	semidirect
585. #121	C₂³×C₇	semidirect
587. C₄×Q₈	C₂³×C₇	semidirect
588. C₄×Q₈	C₂³×C₇	semidirect
589. C₄×Q₈	C₂³×C₇	semidirect
590. C₄×Q₈	C₂³×C₇	semidirect
600. C₄×D₄	C₂³×C₇	semidirect
601. C₄×D₄	C₂³×C₇	semidirect
602. C₄×D₄	C₂³×C₇	semidirect
604. #117	C₂³×C₇	semidirect
605. #117	C₂³×C₇	semidirect
606. #117	C₂³×C₇	semidirect
627. C₂×C₄⋊C₄	C₂³×C₇	semidirect
628. C₂×C₄⋊C₄	C₂³×C₇	semidirect
629. C₂×C₄⋊C₄	C₂³×C₇	semidirect
715. C₂×D₄	C₇×#41	semidirect
806. C₂×C₇	#3520	direct (N × H)
841. D₄	C₂×C₇×#41	semidirect
880. C₇	C₂×#3520	direct (N × H)
919. C₂	C₇×#3520	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×#3520	2
C₂×C₇×#556	2
C₂×C₇×#554	2
C₂×C₇×#552	2
C₂×C₇×#551	2
C₂×C₇×D₄×Q₈	2
C₂×C₇×#548	2
C₂×C₇×#547	2
C₂×C₇×#546	2
C₂×C₇×#542	2
C₂×C₇×#539	2
C₂×C₇×#533	2
C₂×C₇×#529	2
C₂×C₇×#525	2
C₂²×C₇×C₂²⋊Q₈	2
C₂×C₇×#520	2
C₂²×C₄×C₇×D₄	2
C₂×#3520	7

Subgroups — C2×C7×#3520 #13239988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3520 #13239988