Subgroups — C₂×C₇×#3506 #13239985

Order 1792.

7994 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3506	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#559	C₂	1	4	yes	maximal, complemented
3	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#555	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#553	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#550	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#547	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#538	C₂	1	4	yes	maximal, complemented
9	C₂×C₇×#535	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#525	C₂	1	4	yes	maximal, complemented
13	C₂×C₇×#520	C₂	1	2	yes	maximal, complemented
14	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×#41	C₂²	1	2	yes	—
16	C₂²×C₇×#41	C₂²	1	4	yes	complemented
17	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
19	C₇×#559	C₂²	1	64	yes	complemented
20	C₇×#556	C₂²	1	32	yes	complemented
21	C₇×#555	C₂²	1	32	yes	complemented
22	C₇×#553	C₂²	1	64	yes	complemented
23	C₇×#550	C₂²	1	32	yes	complemented
24	C₇×#547	C₂²	1	32	yes	complemented
25	C₇×#538	C₂²	1	64	yes	complemented
26	C₇×#535	C₂²	1	32	yes	complemented
27	C₇×#533	C₂²	1	16	yes	complemented
28	C₇×#532	C₂²	1	16	yes	complemented
29	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₇×#127	C₂²	1	4	yes	—
33	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₇×#126	C₂²	1	8	yes	complemented
35	C₂×C₇×#125	C₂²	1	2	yes	complemented
36	C₂×C₇×#124	C₂²	1	4	yes	—
37	C₂×C₇×#124	C₂²	1	2	yes	complemented
38	C₂×C₇×#124	C₂²	1	8	yes	complemented
39	C₇×#525	C₂²	1	64	yes	complemented
40	C₂×C₇×#123	C₂²	1	8	yes	complemented
41	C₂×C₇×#123	C₂²	1	8	yes	complemented
42	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₂×C₇×#121	C₂²	1	2	yes	—
46	C₂×C₇×#121	C₂²	1	2	yes	—
47	C₂×C₇×#121	C₂²	1	4	yes	—
48	C₂×C₇×#121	C₂²	1	4	yes	—
49	C₂×C₇×#121	C₂²	1	4	yes	complemented
50	C₂×C₇×#121	C₂²	1	8	yes	complemented
51	C₂×C₇×#120	C₂²	1	8	yes	—
52	C₇×#520	C₂²	1	32	yes	complemented
53	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
54	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
55	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
56	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
57	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
58	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
59	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
60	C₂×C₄×C₇×D₄	C₂²	1	8	yes	—
61	C₂×C₄×C₇×D₄	C₂²	1	16	yes	complemented
62	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
63	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
64	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
65	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
66	C₂×C₇×#117	C₂²	1	2	yes	—
67	C₂×C₇×#117	C₂²	1	4	yes	complemented
68	C₂×C₇×#117	C₂²	1	4	yes	complemented
69	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	complemented
71	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
73	C₂×#3506	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂⁵×C₇	C₂³	1	2	yes	—
75	C₂×C₇×#41	—	2	16	no	—
76	C₂×C₇×#41	—	4	16	no	—
77	C₂×C₇×#41	C₂³	1	16	yes	—
78	C₂×C₇×#41	C₂³	1	32	yes	complemented
79	C₂²×C₇×Q₈	C₂³	1	2	yes	—
80	C₂²×C₇×Q₈	C₂³	1	2	yes	—
81	C₂²×C₇×Q₈	C₂³	1	2	yes	—
82	C₂²×C₇×D₄	—	2	8	no	—
83	C₂²×C₇×D₄	C₂³	1	2	yes	—
84	C₂²×C₇×D₄	C₂³	1	2	yes	—
85	C₂²×C₇×D₄	C₂³	1	8	yes	—
86	C₂²×C₇×D₄	C₂³	1	4	yes	—
87	C₂²×C₇×D₄	C₂³	1	2	yes	—
88	C₂²×C₇×D₄	C₂³	1	2	yes	—
89	C₂²×C₇×D₄	C₂³	1	8	yes	—
90	C₂²×C₇×D₄	C₂³	1	8	yes	—
91	C₂²×C₇×D₄	C₂³	1	2	yes	—
92	C₂³×C₄×C₇	—	4	8	no	—
93	C₂³×C₄×C₇	C₂³	1	4	yes	—
94	C₂³×C₄×C₇	C₂³	1	4	yes	—
95	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₇	C₂³	1	8	yes	—
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₇	C₂³	1	4	yes	—
100	C₂³×C₄×C₇	C₂³	1	16	yes	—
101	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
102	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
103	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
104	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
105	C₇×#127	C₂³	1	32	yes	—
106	C₇×#127	C₂³	1	8	yes	complemented
107	C₇×#126	C₂³	1	64	yes	complemented
108	C₇×#125	C₂³	1	16	yes	complemented
109	C₇×#124	C₂³	1	32	yes	—
110	C₇×#124	C₂³	1	16	yes	complemented
111	C₇×#124	C₂³	1	64	yes	complemented
112	C₇×#123	C₂³	1	64	yes	complemented
113	C₇×#123	C₂³	1	64	yes	complemented
114	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
115	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
116	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
117	C₇×#121	C₂³	1	16	yes	—
118	C₇×#121	C₂³	1	16	yes	—
119	C₇×#121	C₂³	1	32	yes	—
120	C₇×#121	C₂³	1	32	yes	—
121	C₇×#121	C₂³	1	32	yes	complemented
122	C₇×#121	C₂³	1	64	yes	complemented
123	C₇×#120	C₂³	1	64	yes	—
124	C₄×C₇×Q₈	C₂³	1	32	yes	complemented
125	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
126	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
127	C₄×C₇×D₄	C₂³	1	16	yes	—
128	C₄×C₇×D₄	C₂³	1	16	yes	—
129	C₄×C₇×D₄	C₂³	1	16	yes	—
130	C₄×C₇×D₄	C₂³	1	16	yes	—
131	C₄×C₇×D₄	C₂³	1	64	yes	—
132	C₄×C₇×D₄	C₂³	1	32	yes	complemented
133	C₄×C₇×D₄	C₂³	1	64	yes	complemented
134	C₄×C₇×D₄	C₂³	1	16	yes	complemented
135	C₄×C₇×D₄	C₂³	1	16	yes	complemented
136	C₇×#117	C₂³	1	16	yes	—
137	C₇×#117	C₂³	1	32	yes	complemented
138	C₇×#117	C₂³	1	32	yes	complemented
139	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	complemented
152	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
155	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
157	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
158	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
160	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₇	C₂³	1	8	yes	—
166	C₂×C₄²×C₇	C₂³	1	4	yes	—
167	C₂×C₄²×C₇	C₂³	1	8	yes	—
168	#3506	C₂×C₇	1	32	yes	direct product factor
169	C₂×#559	C₂×C₇	1	4	yes	complemented
170	C₂×#556	C₂×C₇	1	2	yes	complemented
171	C₂×#555	C₂×C₇	1	2	yes	complemented
172	C₂×#553	C₂×C₇	1	4	yes	complemented
173	C₂×#550	C₂×C₇	1	2	yes	complemented
174	C₂×#547	C₂×C₇	1	2	yes	complemented
175	C₂×#538	C₂×C₇	1	4	yes	complemented
176	C₂×#535	C₂×C₇	1	2	yes	complemented
177	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
178	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
179	C₂×#525	C₂×C₇	1	4	yes	complemented
180	C₂×#520	C₂×C₇	1	2	yes	complemented
181	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
182	C₂⁴×C₇	—	2	8	no	—
183	C₂⁴×C₇	—	4	4	no	—
184	C₂⁴×C₇	—	4	4	no	—
185	C₂⁴×C₇	C₂⁴	1	4	yes	—
186	C₂⁴×C₇	C₂⁴	1	4	yes	—
187	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
188	C₂⁴×C₇	C₂⁴	1	8	yes	—
189	C₇×#41	—	2	64	no	—
190	C₇×#41	—	4	64	no	—
191	C₂×C₇×Q₈	—	2	8	no	—
192	C₂×C₇×Q₈	—	2	8	no	—
193	C₂×C₇×Q₈	—	4	4	no	—
194	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
195	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
196	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
197	C₂×C₇×D₄	—	2	16	no	—
198	C₂×C₇×D₄	—	2	8	no	—
199	C₂×C₇×D₄	—	2	8	no	—
200	C₂×C₇×D₄	—	2	8	no	—
201	C₂×C₇×D₄	—	2	32	no	—
202	C₂×C₇×D₄	—	2	8	no	—
203	C₂×C₇×D₄	—	4	4	no	—
204	C₂×C₇×D₄	—	4	16	no	—
205	C₂×C₇×D₄	—	4	16	no	—
206	C₂×C₇×D₄	C₂⁴	1	16	yes	—
207	C₂×C₇×D₄	C₂⁴	1	8	yes	—
208	C₂×C₇×D₄	C₂⁴	1	8	yes	—
209	C₂×C₇×D₄	C₂⁴	1	8	yes	—
210	C₂×C₇×D₄	C₂⁴	1	8	yes	—
211	C₂×C₇×D₄	C₂⁴	1	32	yes	—
212	C₂×C₇×D₄	C₂⁴	1	8	yes	—
213	C₂×C₇×D₄	C₂⁴	1	32	yes	—
214	C₂²×C₄×C₇	—	2	16	no	—
215	C₂²×C₄×C₇	—	2	4	no	—
216	C₂²×C₄×C₇	—	2	16	no	—
217	C₂²×C₄×C₇	—	4	32	no	—
218	C₂²×C₄×C₇	—	4	4	no	—
219	C₂²×C₄×C₇	—	4	8	no	—
220	C₂²×C₄×C₇	—	4	2	no	—
221	C₂²×C₄×C₇	—	4	16	no	—
222	C₂²×C₄×C₇	#41	1	8	yes	complemented
223	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
225	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
226	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
235	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
236	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
237	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
241	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
242	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
243	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
244	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
245	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
246	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
247	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
248	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
249	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
250	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
251	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
252	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
253	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
254	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
255	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
256	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
257	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
258	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
259	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
260	C₄²×C₇	C₂⁴	1	4	yes	—
261	C₄²×C₇	C₂⁴	1	4	yes	—
262	C₄²×C₇	C₂⁴	1	4	yes	—
263	C₄²×C₇	C₂⁴	1	4	yes	—
264	C₄²×C₇	C₂⁴	1	16	yes	—
265	C₄²×C₇	C₂⁴	1	32	yes	—
266	C₂²×#41	C₂²×C₇	1	2	yes	—
267	C₂²×#41	C₂²×C₇	1	4	yes	complemented
268	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
269	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
270	#559	C₂²×C₇	1	64	yes	complemented
271	#556	C₂²×C₇	1	32	yes	complemented
272	#555	C₂²×C₇	1	32	yes	complemented
273	#553	C₂²×C₇	1	64	yes	complemented
274	#550	C₂²×C₇	1	32	yes	complemented
275	#547	C₂²×C₇	1	32	yes	complemented
276	#538	C₂²×C₇	1	64	yes	complemented
277	#535	C₂²×C₇	1	32	yes	complemented
278	#533	C₂²×C₇	1	16	yes	complemented
279	#532	C₂²×C₇	1	16	yes	complemented
280	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
281	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
282	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
283	C₂×#127	C₂²×C₇	1	4	yes	—
284	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
285	C₂×#126	C₂²×C₇	1	8	yes	complemented
286	C₂×#125	C₂²×C₇	1	2	yes	complemented
287	C₂×#124	C₂²×C₇	1	4	yes	—
288	C₂×#124	C₂²×C₇	1	2	yes	complemented
289	C₂×#124	C₂²×C₇	1	8	yes	complemented
290	#525	C₂²×C₇	1	64	yes	complemented
291	C₂×#123	C₂²×C₇	1	8	yes	complemented
292	C₂×#123	C₂²×C₇	1	8	yes	complemented
293	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
294	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
296	C₂×#121	C₂²×C₇	1	2	yes	—
297	C₂×#121	C₂²×C₇	1	2	yes	—
298	C₂×#121	C₂²×C₇	1	4	yes	—
299	C₂×#121	C₂²×C₇	1	4	yes	—
300	C₂×#121	C₂²×C₇	1	4	yes	complemented
301	C₂×#121	C₂²×C₇	1	8	yes	complemented
302	C₂×#120	C₂²×C₇	1	8	yes	—
303	#520	C₂²×C₇	1	32	yes	complemented
304	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
305	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
306	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
307	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
308	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
309	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
310	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
311	C₂×C₄×D₄	C₂²×C₇	1	8	yes	—
312	C₂×C₄×D₄	C₂²×C₇	1	16	yes	complemented
313	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
314	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
315	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
316	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
317	C₂×#117	C₂²×C₇	1	2	yes	—
318	C₂×#117	C₂²×C₇	1	4	yes	complemented
319	C₂×#117	C₂²×C₇	1	4	yes	complemented
320	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
321	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	complemented
322	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
323	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
324	C₂³×C₇	—	2	2	no	—
325	C₂³×C₇	—	2	2	no	—
326	C₂³×C₇	—	2	8	no	—
327	C₂³×C₇	—	2	16	no	—
328	C₂³×C₇	—	2	8	no	—
329	C₂³×C₇	—	2	8	no	—
330	C₂³×C₇	—	2	8	no	—
331	C₂³×C₇	—	2	8	no	—
332	C₂³×C₇	—	2	8	no	—
333	C₂³×C₇	—	4	8	no	—
334	C₂³×C₇	—	4	8	no	—
335	C₂³×C₇	—	4	32	no	—
336	C₂³×C₇	C₂×#41	1	4	yes	—
337	C₂³×C₇	C₂⁵	1	8	yes	—
338	C₂³×C₇	C₂⁵	1	8	yes	—
339	C₂³×C₇	C₂⁵	1	2	yes	—
340	C₂³×C₇	C₂⁵	1	1	yes	characteristic
341	C₇×Q₈	—	2	16	no	—
342	C₇×Q₈	—	2	16	no	—
343	C₇×Q₈	—	4	8	no	—
344	C₇×D₄	—	2	32	no	—
345	C₇×D₄	—	2	16	no	—
346	C₇×D₄	—	2	16	no	—
347	C₇×D₄	—	2	16	no	—
348	C₇×D₄	—	2	16	no	—
349	C₇×D₄	—	4	8	no	—
350	C₇×D₄	—	4	32	no	—
351	C₇×D₄	—	4	32	no	—
352	C₂×C₄×C₇	—	2	8	no	—
353	C₂×C₄×C₇	—	2	2	no	—
354	C₂×C₄×C₇	—	2	8	no	—
355	C₂×C₄×C₇	—	2	8	no	—
356	C₂×C₄×C₇	—	2	2	no	—
357	C₂×C₄×C₇	—	2	2	no	—
358	C₂×C₄×C₇	—	2	8	no	—
359	C₂×C₄×C₇	—	2	32	no	—
360	C₂×C₄×C₇	—	2	8	no	—
361	C₂×C₄×C₇	—	2	32	no	—
362	C₂×C₄×C₇	—	4	8	no	—
363	C₂×C₄×C₇	—	4	16	no	—
364	C₂×C₄×C₇	—	4	4	no	—
365	C₂×C₄×C₇	—	4	32	no	—
366	C₂×C₄×C₇	C₂×#41	1	4	yes	—
367	C₂×C₄×C₇	C₂×#41	1	4	yes	—
368	C₂×C₄×C₇	C₂×#41	1	16	yes	complemented
369	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
370	C₂×C₄×C₇	C₂⁵	1	8	yes	—
371	C₂×C₄×C₇	C₂⁵	1	2	yes	—
372	C₂×C₄×C₇	C₂⁵	1	8	yes	—
373	C₂×C₄×C₇	C₂⁵	1	2	yes	—
374	C₂×C₄×C₇	C₂⁵	1	2	yes	—
375	C₂×C₄×C₇	C₂⁵	1	8	yes	—
376	C₂×C₄×C₇	C₂⁵	1	8	yes	—
377	C₂×C₄×C₇	C₂⁵	1	2	yes	—
378	C₂×C₄×C₇	C₂⁵	1	2	yes	—
379	C₂×C₄×C₇	C₂⁵	1	2	yes	—
380	C₂⁵	C₂³×C₇	1	2	yes	—
381	C₂×#41	—	2	16	no	—
382	C₂×#41	—	4	16	no	—
383	C₂×#41	C₂³×C₇	1	16	yes	—
384	C₂×#41	C₂³×C₇	1	32	yes	complemented
385	C₂²×Q₈	C₂³×C₇	1	2	yes	—
386	C₂²×Q₈	C₂³×C₇	1	2	yes	—
387	C₂²×Q₈	C₂³×C₇	1	2	yes	—
388	C₂²×D₄	—	2	8	no	—
389	C₂²×D₄	C₂³×C₇	1	4	yes	—
390	C₂²×D₄	C₂³×C₇	1	2	yes	—
391	C₂²×D₄	C₂³×C₇	1	2	yes	—
392	C₂²×D₄	C₂³×C₇	1	2	yes	—
393	C₂²×D₄	C₂³×C₇	1	8	yes	—
394	C₂²×D₄	C₂³×C₇	1	2	yes	—
395	C₂²×D₄	C₂³×C₇	1	8	yes	—
396	C₂²×D₄	C₂³×C₇	1	2	yes	—
397	C₂²×D₄	C₂³×C₇	1	8	yes	—
398	C₂³×C₄	—	4	8	no	—
399	C₂³×C₄	C₂³×C₇	1	4	yes	—
400	C₂³×C₄	C₂³×C₇	1	4	yes	—
401	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₇	1	2	yes	—
404	C₂³×C₄	C₂³×C₇	1	8	yes	—
405	C₂³×C₄	C₂³×C₇	1	4	yes	—
406	C₂³×C₄	C₂³×C₇	1	16	yes	—
407	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
408	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
409	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
410	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
411	#127	C₂³×C₇	1	32	yes	—
412	#127	C₂³×C₇	1	8	yes	complemented
413	#126	C₂³×C₇	1	64	yes	complemented
414	#125	C₂³×C₇	1	16	yes	complemented
415	#124	C₂³×C₇	1	32	yes	—
416	#124	C₂³×C₇	1	16	yes	complemented
417	#124	C₂³×C₇	1	64	yes	complemented
418	#123	C₂³×C₇	1	64	yes	complemented
419	#123	C₂³×C₇	1	64	yes	complemented
420	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
421	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
422	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
423	#121	C₂³×C₇	1	16	yes	—
424	#121	C₂³×C₇	1	16	yes	—
425	#121	C₂³×C₇	1	32	yes	—
426	#121	C₂³×C₇	1	32	yes	—
427	#121	C₂³×C₇	1	32	yes	complemented
428	#121	C₂³×C₇	1	64	yes	complemented
429	#120	C₂³×C₇	1	64	yes	—
430	C₄×Q₈	C₂³×C₇	1	32	yes	complemented
431	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
432	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
433	C₄×D₄	C₂³×C₇	1	16	yes	—
434	C₄×D₄	C₂³×C₇	1	16	yes	—
435	C₄×D₄	C₂³×C₇	1	16	yes	—
436	C₄×D₄	C₂³×C₇	1	16	yes	—
437	C₄×D₄	C₂³×C₇	1	64	yes	—
438	C₄×D₄	C₂³×C₇	1	32	yes	complemented
439	C₄×D₄	C₂³×C₇	1	64	yes	complemented
440	C₄×D₄	C₂³×C₇	1	16	yes	complemented
441	C₄×D₄	C₂³×C₇	1	16	yes	complemented
442	#117	C₂³×C₇	1	16	yes	—
443	#117	C₂³×C₇	1	32	yes	complemented
444	#117	C₂³×C₇	1	32	yes	complemented
445	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
448	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
450	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	complemented
458	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
467	C₂×C₄²	C₂³×C₇	1	4	yes	—
468	C₂×C₄²	C₂³×C₇	1	8	yes	—
469	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₇	1	8	yes	—
474	C₂²×C₇	—	2	2	no	—
475	C₂²×C₇	—	2	2	no	—
476	C₂²×C₇	—	2	8	no	—
477	C₂²×C₇	—	2	8	no	—
478	C₂²×C₇	—	2	8	no	—
479	C₂²×C₇	—	2	8	no	—
480	C₂²×C₇	—	2	8	no	—
481	C₂²×C₇	—	2	8	no	—
482	C₂²×C₇	—	2	8	no	—
483	C₂²×C₇	—	4	32	no	—
484	C₂²×C₇	—	4	16	no	—
485	C₂²×C₇	—	4	16	no	—
486	C₂²×C₇	C₂²×#41	1	4	yes	—
487	C₂²×C₇	C₂²×#41	1	2	yes	—
488	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
489	C₂²×C₇	#585	1	2	yes	—
490	C₂²×C₇	C₂⁶	1	1	yes	characteristic
491	C₄×C₇	—	2	8	no	—
492	C₄×C₇	—	2	2	no	—
493	C₄×C₇	—	2	8	no	—
494	C₄×C₇	—	2	8	no	—
495	C₄×C₇	—	2	2	no	—
496	C₄×C₇	—	2	2	no	—
497	C₄×C₇	—	2	8	no	—
498	C₄×C₇	C₂²×#41	1	4	yes	—
499	C₄×C₇	C₂²×#41	1	4	yes	—
500	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
501	C₂⁴	—	2	8	no	—
502	C₂⁴	—	4	4	no	—
503	C₂⁴	—	4	4	no	—
504	C₂⁴	C₂⁴×C₇	1	4	yes	—
505	C₂⁴	C₂⁴×C₇	1	4	yes	—
506	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
507	C₂⁴	C₂⁴×C₇	1	8	yes	—
508	#41	—	2	64	no	—
509	#41	—	4	64	no	—
510	C₂×Q₈	—	2	8	no	—
511	C₂×Q₈	—	2	8	no	—
512	C₂×Q₈	—	4	4	no	—
513	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
514	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
515	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
516	C₂×D₄	—	2	16	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	8	no	—
519	C₂×D₄	—	2	8	no	—
520	C₂×D₄	—	2	32	no	—
521	C₂×D₄	—	2	8	no	—
522	C₂×D₄	—	4	16	no	—
523	C₂×D₄	—	4	4	no	—
524	C₂×D₄	—	4	16	no	—
525	C₂×D₄	C₂⁴×C₇	1	16	yes	—
526	C₂×D₄	C₂⁴×C₇	1	8	yes	—
527	C₂×D₄	C₂⁴×C₇	1	8	yes	—
528	C₂×D₄	C₂⁴×C₇	1	8	yes	—
529	C₂×D₄	C₂⁴×C₇	1	8	yes	—
530	C₂×D₄	C₂⁴×C₇	1	32	yes	—
531	C₂×D₄	C₂⁴×C₇	1	8	yes	—
532	C₂×D₄	C₂⁴×C₇	1	32	yes	—
533	C₂²×C₄	—	2	16	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	16	no	—
536	C₂²×C₄	—	4	32	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	8	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	16	no	—
541	C₂²×C₄	C₇×#41	1	8	yes	complemented
542	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
551	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
552	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
554	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
555	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
556	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
559	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
560	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
561	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
562	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
563	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
564	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
565	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
566	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
567	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
568	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
569	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
570	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
571	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
572	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
573	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
574	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
575	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
576	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
577	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
578	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
579	C₄²	C₂⁴×C₇	1	4	yes	—
580	C₄²	C₂⁴×C₇	1	4	yes	—
581	C₄²	C₂⁴×C₇	1	4	yes	—
582	C₄²	C₂⁴×C₇	1	4	yes	—
583	C₄²	C₂⁴×C₇	1	16	yes	—
584	C₄²	C₂⁴×C₇	1	32	yes	—
585	C₂×C₇	—	2	4	no	—
586	C₂×C₇	—	4	8	no	—
587	C₂×C₇	—	4	8	no	—
588	C₂×C₇	#3506	1	4	yes	direct product factor
589	C₂×C₇	C₂³×#41	1	1	yes	characteristic
590	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂×C₇	C₂×#585	1	1	yes	characteristic
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	8	no	—
595	C₂³	—	2	16	no	—
596	C₂³	—	2	8	no	—
597	C₂³	—	2	8	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	8	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	4	8	no	—
603	C₂³	—	4	32	no	—
604	C₂³	C₂×C₇×#41	1	4	yes	—
605	C₂³	C₂⁵×C₇	1	8	yes	—
606	C₂³	C₂⁵×C₇	1	8	yes	—
607	C₂³	C₂⁵×C₇	1	2	yes	—
608	C₂³	C₂⁵×C₇	1	1	yes	characteristic
609	Q₈	—	2	16	no	—
610	Q₈	—	2	16	no	—
611	Q₈	—	4	8	no	—
612	D₄	—	2	32	no	—
613	D₄	—	2	16	no	—
614	D₄	—	2	16	no	—
615	D₄	—	2	16	no	—
616	D₄	—	2	16	no	—
617	D₄	—	4	8	no	—
618	D₄	—	4	32	no	—
619	D₄	—	4	32	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	32	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	32	no	—
630	C₂×C₄	—	4	8	no	—
631	C₂×C₄	—	4	16	no	—
632	C₂×C₄	—	4	4	no	—
633	C₂×C₄	—	4	32	no	—
634	C₂×C₄	C₂×C₇×#41	1	4	yes	—
635	C₂×C₄	C₂×C₇×#41	1	4	yes	—
636	C₂×C₄	C₂×C₇×#41	1	16	yes	complemented
637	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
638	C₂×C₄	C₂⁵×C₇	1	8	yes	—
639	C₂×C₄	C₂⁵×C₇	1	2	yes	—
640	C₂×C₄	C₂⁵×C₇	1	8	yes	—
641	C₂×C₄	C₂⁵×C₇	1	2	yes	—
642	C₂×C₄	C₂⁵×C₇	1	2	yes	—
643	C₂×C₄	C₂⁵×C₇	1	8	yes	—
644	C₂×C₄	C₂⁵×C₇	1	8	yes	—
645	C₂×C₄	C₂⁵×C₇	1	2	yes	—
646	C₂×C₄	C₂⁵×C₇	1	2	yes	—
647	C₂×C₄	C₂⁵×C₇	1	2	yes	—
648	C₇	C₂×#3506	1	1	yes	characteristic, direct product factor, Sylow
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	8	no	—
652	C₂²	—	2	8	no	—
653	C₂²	—	2	8	no	—
654	C₂²	—	2	8	no	—
655	C₂²	—	2	8	no	—
656	C₂²	—	2	8	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	4	32	no	—
659	C₂²	—	4	16	no	—
660	C₂²	—	4	16	no	—
661	C₂²	C₂²×C₇×#41	1	4	yes	—
662	C₂²	C₂²×C₇×#41	1	2	yes	—
663	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
664	C₂²	C₇×#585	1	2	yes	—
665	C₂²	C₂⁶×C₇	1	1	yes	characteristic
666	C₄	—	2	8	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	8	no	—
669	C₄	—	2	8	no	—
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	8	no	—
673	C₄	C₂²×C₇×#41	1	4	yes	—
674	C₄	C₂²×C₇×#41	1	4	yes	—
675	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
676	C₂	—	2	4	no	—
677	C₂	—	4	8	no	—
678	C₂	—	4	8	no	—
679	C₂	C₇×#3506	1	4	yes	direct product factor
680	C₂	C₂³×C₇×#41	1	1	yes	characteristic
681	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
682	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×#3506	C₂	direct (N × H)
2. C₂×C₇×#559	C₂	semidirect
3. C₂×C₇×#556	C₂	semidirect
4. C₂×C₇×#555	C₂	semidirect
5. C₂×C₇×#553	C₂	semidirect
6. C₂×C₇×#550	C₂	semidirect
7. C₂×C₇×#547	C₂	semidirect
8. C₂×C₇×#538	C₂	semidirect
9. C₂×C₇×#535	C₂	semidirect
10. C₂×C₇×#533	C₂	semidirect
11. C₂×C₇×#532	C₂	semidirect
12. C₂×C₇×#525	C₂	semidirect
13. C₂×C₇×#520	C₂	semidirect
14. C₂²×C₄×C₇×D₄	C₂	semidirect
16. C₂²×C₇×#41	C₂²	semidirect
19. C₇×#559	C₂²	semidirect
20. C₇×#556	C₂²	semidirect
21. C₇×#555	C₂²	semidirect
22. C₇×#553	C₂²	semidirect
23. C₇×#550	C₂²	semidirect
24. C₇×#547	C₂²	semidirect
25. C₇×#538	C₂²	semidirect
26. C₇×#535	C₂²	semidirect
27. C₇×#533	C₂²	semidirect
28. C₇×#532	C₂²	semidirect
29. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₇×#127	C₂²	semidirect
34. C₂×C₇×#126	C₂²	semidirect
35. C₂×C₇×#125	C₂²	semidirect
37. C₂×C₇×#124	C₂²	semidirect
38. C₂×C₇×#124	C₂²	semidirect
39. C₇×#525	C₂²	semidirect
40. C₂×C₇×#123	C₂²	semidirect
41. C₂×C₇×#123	C₂²	semidirect
44. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₇×#121	C₂²	semidirect
50. C₂×C₇×#121	C₂²	semidirect
52. C₇×#520	C₂²	semidirect
53. C₂×C₄×C₇×Q₈	C₂²	semidirect
54. C₂×C₄×C₇×Q₈	C₂²	semidirect
55. C₂×C₄×C₇×Q₈	C₂²	semidirect
61. C₂×C₄×C₇×D₄	C₂²	semidirect
62. C₂×C₄×C₇×D₄	C₂²	semidirect
63. C₂×C₄×C₇×D₄	C₂²	semidirect
64. C₂×C₄×C₇×D₄	C₂²	semidirect
65. C₂×C₄×C₇×D₄	C₂²	semidirect
67. C₂×C₇×#117	C₂²	semidirect
68. C₂×C₇×#117	C₂²	semidirect
70. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
73. C₂×#3506	C₇	direct (N × H)
78. C₂×C₇×#41	C₂³	semidirect
102. C₇×C₄⋊Q₈	C₂³	semidirect
103. C₇×C₄⋊Q₈	C₂³	semidirect
104. C₇×C₄⋊Q₈	C₂³	semidirect
106. C₇×#127	C₂³	semidirect
107. C₇×#126	C₂³	semidirect
108. C₇×#125	C₂³	semidirect
110. C₇×#124	C₂³	semidirect
111. C₇×#124	C₂³	semidirect
112. C₇×#123	C₂³	semidirect
113. C₇×#123	C₂³	semidirect
116. C₇×C₂²⋊Q₈	C₂³	semidirect
121. C₇×#121	C₂³	semidirect
122. C₇×#121	C₂³	semidirect
124. C₄×C₇×Q₈	C₂³	semidirect
125. C₄×C₇×Q₈	C₂³	semidirect
126. C₄×C₇×Q₈	C₂³	semidirect
132. C₄×C₇×D₄	C₂³	semidirect
133. C₄×C₇×D₄	C₂³	semidirect
134. C₄×C₇×D₄	C₂³	semidirect
135. C₄×C₇×D₄	C₂³	semidirect
137. C₇×#117	C₂³	semidirect
138. C₇×#117	C₂³	semidirect
151. C₂×C₇×C₄⋊C₄	C₂³	semidirect
168. #3506	C₂×C₇	direct (N × H)
169. C₂×#559	C₂×C₇	semidirect
170. C₂×#556	C₂×C₇	semidirect
171. C₂×#555	C₂×C₇	semidirect
172. C₂×#553	C₂×C₇	semidirect
173. C₂×#550	C₂×C₇	semidirect
174. C₂×#547	C₂×C₇	semidirect
175. C₂×#538	C₂×C₇	semidirect
176. C₂×#535	C₂×C₇	semidirect
177. C₂×#533	C₂×C₇	semidirect
178. C₂×#532	C₂×C₇	semidirect
179. C₂×#525	C₂×C₇	semidirect
180. C₂×#520	C₂×C₇	semidirect
181. C₂²×C₄×D₄	C₂×C₇	semidirect
222. C₂²×C₄×C₇	#41	semidirect
267. C₂²×#41	C₂²×C₇	semidirect
270. #559	C₂²×C₇	semidirect
271. #556	C₂²×C₇	semidirect
272. #555	C₂²×C₇	semidirect
273. #553	C₂²×C₇	semidirect
274. #550	C₂²×C₇	semidirect
275. #547	C₂²×C₇	semidirect
276. #538	C₂²×C₇	semidirect
277. #535	C₂²×C₇	semidirect
278. #533	C₂²×C₇	semidirect
279. #532	C₂²×C₇	semidirect
280. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
281. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
282. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
284. C₂×#127	C₂²×C₇	semidirect
285. C₂×#126	C₂²×C₇	semidirect
286. C₂×#125	C₂²×C₇	semidirect
288. C₂×#124	C₂²×C₇	semidirect
289. C₂×#124	C₂²×C₇	semidirect
290. #525	C₂²×C₇	semidirect
291. C₂×#123	C₂²×C₇	semidirect
292. C₂×#123	C₂²×C₇	semidirect
295. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
300. C₂×#121	C₂²×C₇	semidirect
301. C₂×#121	C₂²×C₇	semidirect
303. #520	C₂²×C₇	semidirect
304. C₂×C₄×Q₈	C₂²×C₇	semidirect
305. C₂×C₄×Q₈	C₂²×C₇	semidirect
306. C₂×C₄×Q₈	C₂²×C₇	semidirect
312. C₂×C₄×D₄	C₂²×C₇	semidirect
313. C₂×C₄×D₄	C₂²×C₇	semidirect
314. C₂×C₄×D₄	C₂²×C₇	semidirect
315. C₂×C₄×D₄	C₂²×C₇	semidirect
316. C₂×C₄×D₄	C₂²×C₇	semidirect
318. C₂×#117	C₂²×C₇	semidirect
319. C₂×#117	C₂²×C₇	semidirect
321. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
368. C₂×C₄×C₇	C₂×#41	semidirect
384. C₂×#41	C₂³×C₇	semidirect
408. C₄⋊Q₈	C₂³×C₇	semidirect
409. C₄⋊Q₈	C₂³×C₇	semidirect
410. C₄⋊Q₈	C₂³×C₇	semidirect
412. #127	C₂³×C₇	semidirect
413. #126	C₂³×C₇	semidirect
414. #125	C₂³×C₇	semidirect
416. #124	C₂³×C₇	semidirect
417. #124	C₂³×C₇	semidirect
418. #123	C₂³×C₇	semidirect
419. #123	C₂³×C₇	semidirect
422. C₂²⋊Q₈	C₂³×C₇	semidirect
427. #121	C₂³×C₇	semidirect
428. #121	C₂³×C₇	semidirect
430. C₄×Q₈	C₂³×C₇	semidirect
431. C₄×Q₈	C₂³×C₇	semidirect
432. C₄×Q₈	C₂³×C₇	semidirect
438. C₄×D₄	C₂³×C₇	semidirect
439. C₄×D₄	C₂³×C₇	semidirect
440. C₄×D₄	C₂³×C₇	semidirect
441. C₄×D₄	C₂³×C₇	semidirect
443. #117	C₂³×C₇	semidirect
444. #117	C₂³×C₇	semidirect
457. C₂×C₄⋊C₄	C₂³×C₇	semidirect
541. C₂²×C₄	C₇×#41	semidirect
588. C₂×C₇	#3506	direct (N × H)
636. C₂×C₄	C₂×C₇×#41	semidirect
648. C₇	C₂×#3506	direct (N × H)
679. C₂	C₇×#3506	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×#3506	2
C₂×C₇×#559	2
C₂×C₇×#556	2
C₂×C₇×#555	2
C₂×C₇×#553	2
C₂×C₇×#550	2
C₂×C₇×#547	2
C₂×C₇×#538	2
C₂×C₇×#535	2
C₂×C₇×#533	2
C₂×C₇×#532	2
C₂×C₇×#525	2
C₂×C₇×#520	2
C₂²×C₄×C₇×D₄	2
C₂×#3506	7

Subgroups — C2×C7×#3506 #13239985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3506 #13239985