Subgroups — C₂×C₇×#3543 #13239960

Order 1792.

8814 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3543	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#560	C₂	1	4	yes	maximal, complemented
3	C₂×C₇×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#550	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#546	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×D₄²	C₂	1	4	yes	maximal, complemented
7	C₂×C₇×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#540	C₂	1	4	yes	maximal, complemented
9	C₂×C₇×#535	C₂	1	4	yes	maximal, complemented
10	C₂×C₇×#534	C₂	1	4	yes	maximal, complemented
11	C₂²×C₇×#127	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×#41	C₂²	1	4	yes	complemented
14	C₂³×C₇×D₄	C₂²	1	2	yes	complemented
15	C₂³×C₇×D₄	C₂²	1	4	yes	complemented
16	C₂³×C₇×D₄	C₂²	1	4	yes	complemented
17	C₂³×C₇×D₄	C₂²	1	4	yes	complemented
18	C₇×#560	C₂²	1	64	yes	complemented
19	C₇×#559	C₂²	1	16	yes	complemented
20	C₇×#550	C₂²	1	32	yes	complemented
21	C₇×#546	C₂²	1	64	yes	complemented
22	C₇×D₄²	C₂²	1	64	yes	complemented
23	C₇×D₄²	C₂²	1	16	yes	complemented
24	C₇×#540	C₂²	1	64	yes	complemented
25	C₇×#535	C₂²	1	64	yes	complemented
26	C₇×#534	C₂²	1	64	yes	complemented
27	C₂×C₇×#127	C₂²	1	1	yes	characteristic
28	C₂×C₇×#127	C₂²	1	4	yes	complemented
29	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₇×#127	C₂²	1	2	yes	complemented
31	C₂×C₇×#127	C₂²	1	4	yes	complemented
32	C₂×C₇×#127	C₂²	1	16	yes	complemented
33	C₇×#529	C₂²	1	32	yes	complemented
34	C₂×C₇×#126	C₂²	1	4	yes	complemented
35	C₂×C₇×#125	C₂²	1	2	yes	complemented
36	C₂×C₇×#124	C₂²	1	2	yes	complemented
37	C₂×C₇×#124	C₂²	1	4	yes	complemented
38	C₂×C₇×#123	C₂²	1	4	yes	complemented
39	C₂×C₇×#123	C₂²	1	4	yes	complemented
40	C₂×C₇×#123	C₂²	1	4	yes	complemented
41	C₂×C₇×#123	C₂²	1	8	yes	complemented
42	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
43	C₂×C₇×#121	C₂²	1	2	yes	—
44	C₂×C₇×#121	C₂²	1	8	yes	complemented
45	C₂×C₇×#121	C₂²	1	8	yes	complemented
46	C₂×C₇×#121	C₂²	1	8	yes	complemented
47	C₂×C₇×#121	C₂²	1	4	yes	complemented
48	C₂×C₇×#121	C₂²	1	4	yes	complemented
49	C₂×C₇×#121	C₂²	1	8	yes	complemented
50	C₂×C₇×#120	C₂²	1	4	yes	complemented
51	C₂×C₇×#120	C₂²	1	8	yes	complemented
52	C₂×C₇×#120	C₂²	1	4	yes	complemented
53	C₂×C₇×#120	C₂²	1	8	yes	complemented
54	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
55	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
56	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
57	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
58	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
59	C₂×C₇×#117	C₂²	1	4	yes	complemented
60	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
61	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×#3543	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂⁵×C₇	C₂³	1	4	yes	—
64	C₂⁵×C₇	C₂³	1	4	yes	—
65	C₂×C₇×#41	—	4	16	no	—
66	C₂×C₇×#41	C₂³	1	32	yes	complemented
67	C₂²×C₇×Q₈	C₂³	1	2	yes	—
68	C₂²×C₇×D₄	—	4	16	no	—
69	C₂²×C₇×D₄	—	4	16	no	—
70	C₂²×C₇×D₄	—	4	8	no	—
71	C₂²×C₇×D₄	—	4	16	no	—
72	C₂²×C₇×D₄	C₂³	1	4	yes	—
73	C₂²×C₇×D₄	C₂³	1	2	yes	—
74	C₂²×C₇×D₄	C₂³	1	4	yes	—
75	C₂²×C₇×D₄	C₂³	1	4	yes	—
76	C₂²×C₇×D₄	C₂³	1	8	yes	—
77	C₂²×C₇×D₄	C₂³	1	2	yes	—
78	C₂²×C₇×D₄	C₂³	1	8	yes	—
79	C₂²×C₇×D₄	C₂³	1	4	yes	—
80	C₂²×C₇×D₄	C₂³	1	8	yes	—
81	C₂²×C₇×D₄	C₂³	1	2	yes	—
82	C₂²×C₇×D₄	C₂³	1	8	yes	—
83	C₂²×C₇×D₄	C₂³	1	16	yes	complemented
84	C₂²×C₇×D₄	C₂³	1	32	yes	complemented
85	C₂²×C₇×D₄	C₂³	1	32	yes	complemented
86	C₂²×C₇×D₄	C₂³	1	32	yes	complemented
87	C₂³×C₄×C₇	C₂³	1	2	yes	—
88	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₇	C₂³	1	4	yes	—
91	C₂³×C₄×C₇	C₂³	1	8	yes	—
92	C₇×#127	C₂³	1	8	yes	—
93	C₇×#127	C₂³	1	32	yes	complemented
94	C₇×#127	C₂³	1	8	yes	complemented
95	C₇×#127	C₂³	1	16	yes	complemented
96	C₇×#127	C₂³	1	32	yes	complemented
97	C₇×#126	C₂³	1	32	yes	complemented
98	C₇×#125	C₂³	1	16	yes	complemented
99	C₇×#124	C₂³	1	16	yes	complemented
100	C₇×#124	C₂³	1	32	yes	complemented
101	C₇×#123	C₂³	1	32	yes	complemented
102	C₇×#123	C₂³	1	32	yes	complemented
103	C₇×#123	C₂³	1	32	yes	complemented
104	C₇×#123	C₂³	1	64	yes	complemented
105	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
106	C₇×#121	C₂³	1	16	yes	—
107	C₇×#121	C₂³	1	64	yes	complemented
108	C₇×#121	C₂³	1	64	yes	complemented
109	C₇×#121	C₂³	1	64	yes	complemented
110	C₇×#121	C₂³	1	32	yes	complemented
111	C₇×#121	C₂³	1	32	yes	complemented
112	C₇×#121	C₂³	1	64	yes	complemented
113	C₇×#120	C₂³	1	32	yes	complemented
114	C₇×#120	C₂³	1	64	yes	complemented
115	C₇×#120	C₂³	1	32	yes	complemented
116	C₇×#120	C₂³	1	64	yes	complemented
117	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
118	C₄×C₇×D₄	C₂³	1	32	yes	complemented
119	C₄×C₇×D₄	C₂³	1	16	yes	complemented
120	C₄×C₇×D₄	C₂³	1	32	yes	complemented
121	C₄×C₇×D₄	C₂³	1	32	yes	complemented
122	C₇×#117	C₂³	1	32	yes	complemented
123	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
137	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
138	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
139	C₂×C₄²×C₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₇	C₂³	1	4	yes	—
143	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
144	#3543	C₂×C₇	1	32	yes	direct product factor
145	C₂×#560	C₂×C₇	1	4	yes	complemented
146	C₂×#559	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#550	C₂×C₇	1	2	yes	complemented
148	C₂×#546	C₂×C₇	1	4	yes	complemented
149	C₂×D₄²	C₂×C₇	1	4	yes	complemented
150	C₂×D₄²	C₂×C₇	1	1	yes	characteristic, complemented
151	C₂×#540	C₂×C₇	1	4	yes	complemented
152	C₂×#535	C₂×C₇	1	4	yes	complemented
153	C₂×#534	C₂×C₇	1	4	yes	complemented
154	C₂²×#127	C₂×C₇	1	1	yes	characteristic, complemented
155	C₂×#529	C₂×C₇	1	2	yes	complemented
156	C₂⁴×C₇	—	2	16	no	—
157	C₂⁴×C₇	—	4	16	no	—
158	C₂⁴×C₇	—	4	16	no	—
159	C₂⁴×C₇	—	4	8	no	—
160	C₂⁴×C₇	C₂⁴	1	4	yes	—
161	C₂⁴×C₇	C₂⁴	1	4	yes	—
162	C₂⁴×C₇	C₂⁴	1	4	yes	—
163	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₇	C₂⁴	1	16	yes	—
165	C₂⁴×C₇	C₂⁴	1	16	yes	—
166	C₇×#41	—	4	64	no	—
167	C₂×C₇×Q₈	—	2	8	no	—
168	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
169	C₂×C₇×D₄	—	2	16	no	—
170	C₂×C₇×D₄	—	2	8	no	—
171	C₂×C₇×D₄	—	2	16	no	—
172	C₂×C₇×D₄	—	2	16	no	—
173	C₂×C₇×D₄	—	4	64	no	—
174	C₂×C₇×D₄	—	4	64	no	—
175	C₂×C₇×D₄	—	4	16	no	—
176	C₂×C₇×D₄	—	4	16	no	—
177	C₂×C₇×D₄	—	4	4	no	—
178	C₂×C₇×D₄	—	4	8	no	—
179	C₂×C₇×D₄	—	4	4	no	—
180	C₂×C₇×D₄	—	4	16	no	—
181	C₂×C₇×D₄	—	4	32	no	—
182	C₂×C₇×D₄	—	4	16	no	—
183	C₂×C₇×D₄	—	4	64	no	—
184	C₂×C₇×D₄	C₂⁴	1	16	yes	—
185	C₂×C₇×D₄	C₂⁴	1	8	yes	—
186	C₂×C₇×D₄	C₂⁴	1	16	yes	—
187	C₂×C₇×D₄	C₂⁴	1	16	yes	—
188	C₂×C₇×D₄	C₂⁴	1	32	yes	—
189	C₂×C₇×D₄	C₂⁴	1	32	yes	—
190	C₂×C₇×D₄	C₂⁴	1	8	yes	—
191	C₂×C₇×D₄	C₂⁴	1	32	yes	—
192	C₂×C₇×D₄	C₂⁴	1	16	yes	—
193	C₂×C₇×D₄	C₂⁴	1	32	yes	—
194	C₂×C₇×D₄	C₂⁴	1	8	yes	—
195	C₂²×C₄×C₇	—	2	4	no	—
196	C₂²×C₄×C₇	—	2	8	no	—
197	C₂²×C₄×C₇	—	2	16	no	—
198	C₂²×C₄×C₇	—	4	8	no	—
199	C₂²×C₄×C₇	—	4	16	no	—
200	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
201	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
203	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
210	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
211	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
212	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
213	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
214	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
215	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
216	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
217	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
218	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
219	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
220	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
221	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
222	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
223	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
224	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
225	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
226	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
227	C₄²×C₇	C₂⁴	1	8	yes	—
228	C₄²×C₇	C₂⁴	1	4	yes	—
229	C₄²×C₇	C₂⁴	1	4	yes	—
230	C₄²×C₇	C₂⁴	1	16	yes	—
231	C₂²×#41	C₂²×C₇	1	4	yes	complemented
232	C₂³×D₄	C₂²×C₇	1	2	yes	complemented
233	C₂³×D₄	C₂²×C₇	1	4	yes	complemented
234	C₂³×D₄	C₂²×C₇	1	4	yes	complemented
235	C₂³×D₄	C₂²×C₇	1	4	yes	complemented
236	#560	C₂²×C₇	1	64	yes	complemented
237	#559	C₂²×C₇	1	16	yes	complemented
238	#550	C₂²×C₇	1	32	yes	complemented
239	#546	C₂²×C₇	1	64	yes	complemented
240	D₄²	C₂²×C₇	1	64	yes	complemented
241	D₄²	C₂²×C₇	1	16	yes	complemented
242	#540	C₂²×C₇	1	64	yes	complemented
243	#535	C₂²×C₇	1	64	yes	complemented
244	#534	C₂²×C₇	1	64	yes	complemented
245	C₂×#127	C₂²×C₇	1	1	yes	characteristic
246	C₂×#127	C₂²×C₇	1	4	yes	complemented
247	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
248	C₂×#127	C₂²×C₇	1	2	yes	complemented
249	C₂×#127	C₂²×C₇	1	4	yes	complemented
250	C₂×#127	C₂²×C₇	1	16	yes	complemented
251	#529	C₂²×C₇	1	32	yes	complemented
252	C₂×#126	C₂²×C₇	1	4	yes	complemented
253	C₂×#125	C₂²×C₇	1	2	yes	complemented
254	C₂×#124	C₂²×C₇	1	2	yes	complemented
255	C₂×#124	C₂²×C₇	1	4	yes	complemented
256	C₂×#123	C₂²×C₇	1	4	yes	complemented
257	C₂×#123	C₂²×C₇	1	4	yes	complemented
258	C₂×#123	C₂²×C₇	1	4	yes	complemented
259	C₂×#123	C₂²×C₇	1	8	yes	complemented
260	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
261	C₂×#121	C₂²×C₇	1	2	yes	—
262	C₂×#121	C₂²×C₇	1	8	yes	complemented
263	C₂×#121	C₂²×C₇	1	8	yes	complemented
264	C₂×#121	C₂²×C₇	1	8	yes	complemented
265	C₂×#121	C₂²×C₇	1	4	yes	complemented
266	C₂×#121	C₂²×C₇	1	4	yes	complemented
267	C₂×#121	C₂²×C₇	1	8	yes	complemented
268	C₂×#120	C₂²×C₇	1	4	yes	complemented
269	C₂×#120	C₂²×C₇	1	8	yes	complemented
270	C₂×#120	C₂²×C₇	1	4	yes	complemented
271	C₂×#120	C₂²×C₇	1	8	yes	complemented
272	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
273	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
274	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
275	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
276	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
277	C₂×#117	C₂²×C₇	1	4	yes	complemented
278	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
279	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
280	C₂³×C₇	—	2	4	no	—
281	C₂³×C₇	—	2	8	no	—
282	C₂³×C₇	—	2	16	no	—
283	C₂³×C₇	—	2	8	no	—
284	C₂³×C₇	—	2	8	no	—
285	C₂³×C₇	—	2	8	no	—
286	C₂³×C₇	—	2	16	no	—
287	C₂³×C₇	—	2	8	no	—
288	C₂³×C₇	—	2	32	no	—
289	C₂³×C₇	—	4	32	no	—
290	C₂³×C₇	—	4	32	no	—
291	C₂³×C₇	—	4	16	no	—
292	C₂³×C₇	—	8	32	no	—
293	C₂³×C₇	—	8	32	no	—
294	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
295	C₂³×C₇	C₂⁵	1	8	yes	—
296	C₂³×C₇	C₂⁵	1	8	yes	—
297	C₂³×C₇	C₂⁵	1	8	yes	—
298	C₂³×C₇	C₂⁵	1	2	yes	—
299	C₂³×C₇	C₂⁵	1	1	yes	characteristic
300	C₇×Q₈	—	2	16	no	—
301	C₇×D₄	—	2	32	no	—
302	C₇×D₄	—	2	16	no	—
303	C₇×D₄	—	2	32	no	—
304	C₇×D₄	—	2	32	no	—
305	C₇×D₄	—	4	32	no	—
306	C₇×D₄	—	4	32	no	—
307	C₇×D₄	—	4	8	no	—
308	C₇×D₄	—	4	16	no	—
309	C₇×D₄	—	4	8	no	—
310	C₇×D₄	—	4	32	no	—
311	C₇×D₄	—	4	32	no	—
312	C₂×C₄×C₇	—	2	8	no	—
313	C₂×C₄×C₇	—	2	8	no	—
314	C₂×C₄×C₇	—	2	2	no	—
315	C₂×C₄×C₇	—	2	2	no	—
316	C₂×C₄×C₇	—	2	4	no	—
317	C₂×C₄×C₇	—	2	8	no	—
318	C₂×C₄×C₇	—	2	8	no	—
319	C₂×C₄×C₇	—	2	16	no	—
320	C₂×C₄×C₇	—	2	32	no	—
321	C₂×C₄×C₇	—	4	16	no	—
322	C₂×C₄×C₇	—	4	32	no	—
323	C₂×C₄×C₇	H(5,𝔽₂)	1	8	yes	—
324	C₂×C₄×C₇	C₂⁵	1	2	yes	—
325	C₂×C₄×C₇	C₂⁵	1	4	yes	—
326	C₂×C₄×C₇	C₂⁵	1	2	yes	—
327	C₂×C₄×C₇	C₂⁵	1	8	yes	—
328	C₂×C₄×C₇	C₂⁵	1	8	yes	—
329	C₂×C₄×C₇	C₂⁵	1	8	yes	—
330	C₂×C₄×C₇	C₂⁵	1	4	yes	—
331	C₂⁵	C₂³×C₇	1	4	yes	—
332	C₂⁵	C₂³×C₇	1	4	yes	—
333	C₂×#41	—	4	16	no	—
334	C₂×#41	C₂³×C₇	1	32	yes	complemented
335	C₂²×Q₈	C₂³×C₇	1	2	yes	—
336	C₂²×D₄	—	4	16	no	—
337	C₂²×D₄	—	4	16	no	—
338	C₂²×D₄	—	4	8	no	—
339	C₂²×D₄	—	4	16	no	—
340	C₂²×D₄	C₂³×C₇	1	4	yes	—
341	C₂²×D₄	C₂³×C₇	1	2	yes	—
342	C₂²×D₄	C₂³×C₇	1	4	yes	—
343	C₂²×D₄	C₂³×C₇	1	4	yes	—
344	C₂²×D₄	C₂³×C₇	1	8	yes	—
345	C₂²×D₄	C₂³×C₇	1	8	yes	—
346	C₂²×D₄	C₂³×C₇	1	2	yes	—
347	C₂²×D₄	C₂³×C₇	1	8	yes	—
348	C₂²×D₄	C₂³×C₇	1	4	yes	—
349	C₂²×D₄	C₂³×C₇	1	8	yes	—
350	C₂²×D₄	C₂³×C₇	1	2	yes	—
351	C₂²×D₄	C₂³×C₇	1	16	yes	complemented
352	C₂²×D₄	C₂³×C₇	1	32	yes	complemented
353	C₂²×D₄	C₂³×C₇	1	32	yes	complemented
354	C₂²×D₄	C₂³×C₇	1	32	yes	complemented
355	C₂³×C₄	C₂³×C₇	1	4	yes	—
356	C₂³×C₄	C₂³×C₇	1	2	yes	—
357	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₇	1	8	yes	—
359	C₂³×C₄	C₂³×C₇	1	4	yes	—
360	#127	C₂³×C₇	1	8	yes	—
361	#127	C₂³×C₇	1	32	yes	complemented
362	#127	C₂³×C₇	1	8	yes	complemented
363	#127	C₂³×C₇	1	16	yes	complemented
364	#127	C₂³×C₇	1	32	yes	complemented
365	#126	C₂³×C₇	1	32	yes	complemented
366	#125	C₂³×C₇	1	16	yes	complemented
367	#124	C₂³×C₇	1	16	yes	complemented
368	#124	C₂³×C₇	1	32	yes	complemented
369	#123	C₂³×C₇	1	32	yes	complemented
370	#123	C₂³×C₇	1	32	yes	complemented
371	#123	C₂³×C₇	1	32	yes	complemented
372	#123	C₂³×C₇	1	64	yes	complemented
373	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
374	#121	C₂³×C₇	1	16	yes	—
375	#121	C₂³×C₇	1	64	yes	complemented
376	#121	C₂³×C₇	1	64	yes	complemented
377	#121	C₂³×C₇	1	64	yes	complemented
378	#121	C₂³×C₇	1	32	yes	complemented
379	#121	C₂³×C₇	1	32	yes	complemented
380	#121	C₂³×C₇	1	64	yes	complemented
381	#120	C₂³×C₇	1	32	yes	complemented
382	#120	C₂³×C₇	1	64	yes	complemented
383	#120	C₂³×C₇	1	32	yes	complemented
384	#120	C₂³×C₇	1	64	yes	complemented
385	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
386	C₄×D₄	C₂³×C₇	1	32	yes	complemented
387	C₄×D₄	C₂³×C₇	1	16	yes	complemented
388	C₄×D₄	C₂³×C₇	1	32	yes	complemented
389	C₄×D₄	C₂³×C₇	1	32	yes	complemented
390	#117	C₂³×C₇	1	32	yes	complemented
391	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
407	C₂×C₄²	C₂³×C₇	1	2	yes	—
408	C₂×C₄²	C₂³×C₇	1	4	yes	—
409	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
412	C₂²×C₇	—	2	4	no	—
413	C₂²×C₇	—	2	8	no	—
414	C₂²×C₇	—	2	8	no	—
415	C₂²×C₇	—	2	16	no	—
416	C₂²×C₇	—	2	8	no	—
417	C₂²×C₇	—	2	8	no	—
418	C₂²×C₇	—	2	8	no	—
419	C₂²×C₇	—	2	16	no	—
420	C₂²×C₇	—	2	8	no	—
421	C₂²×C₇	—	4	16	no	—
422	C₂²×C₇	—	4	16	no	—
423	C₂²×C₇	—	4	16	no	—
424	C₂²×C₇	—	8	32	no	—
425	C₂²×C₇	—	8	32	no	—
426	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
427	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
428	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
429	C₂²×C₇	C₂⁶	1	1	yes	characteristic
430	C₄×C₇	—	2	8	no	—
431	C₄×C₇	—	2	2	no	—
432	C₄×C₇	—	2	2	no	—
433	C₄×C₇	—	2	4	no	—
434	C₄×C₇	—	2	8	no	—
435	C₄×C₇	—	2	8	no	—
436	C₄×C₇	C₂×H(5,𝔽₂)	1	8	yes	—
437	C₂⁴	—	2	16	no	—
438	C₂⁴	—	4	16	no	—
439	C₂⁴	—	4	16	no	—
440	C₂⁴	—	4	8	no	—
441	C₂⁴	C₂⁴×C₇	1	4	yes	—
442	C₂⁴	C₂⁴×C₇	1	4	yes	—
443	C₂⁴	C₂⁴×C₇	1	4	yes	—
444	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
445	C₂⁴	C₂⁴×C₇	1	16	yes	—
446	C₂⁴	C₂⁴×C₇	1	16	yes	—
447	#41	—	4	64	no	—
448	C₂×Q₈	—	2	8	no	—
449	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
450	C₂×D₄	—	2	16	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	16	no	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	4	64	no	—
455	C₂×D₄	—	4	64	no	—
456	C₂×D₄	—	4	16	no	—
457	C₂×D₄	—	4	16	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	4	8	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	16	no	—
462	C₂×D₄	—	4	32	no	—
463	C₂×D₄	—	4	16	no	—
464	C₂×D₄	—	4	64	no	—
465	C₂×D₄	C₂⁴×C₇	1	16	yes	—
466	C₂×D₄	C₂⁴×C₇	1	8	yes	—
467	C₂×D₄	C₂⁴×C₇	1	16	yes	—
468	C₂×D₄	C₂⁴×C₇	1	16	yes	—
469	C₂×D₄	C₂⁴×C₇	1	32	yes	—
470	C₂×D₄	C₂⁴×C₇	1	32	yes	—
471	C₂×D₄	C₂⁴×C₇	1	8	yes	—
472	C₂×D₄	C₂⁴×C₇	1	32	yes	—
473	C₂×D₄	C₂⁴×C₇	1	16	yes	—
474	C₂×D₄	C₂⁴×C₇	1	32	yes	—
475	C₂×D₄	C₂⁴×C₇	1	8	yes	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	16	no	—
479	C₂²×C₄	—	4	8	no	—
480	C₂²×C₄	—	4	16	no	—
481	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
487	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
490	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
491	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
492	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
493	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
494	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
495	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
496	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
497	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
498	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
499	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
500	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
501	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
502	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
503	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
504	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
505	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
506	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
507	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
508	C₄²	C₂⁴×C₇	1	8	yes	—
509	C₄²	C₂⁴×C₇	1	4	yes	—
510	C₄²	C₂⁴×C₇	1	4	yes	—
511	C₄²	C₂⁴×C₇	1	16	yes	—
512	C₂×C₇	—	2	4	no	—
513	C₂×C₇	—	4	8	no	—
514	C₂×C₇	—	4	8	no	—
515	C₂×C₇	—	4	8	no	—
516	C₂×C₇	#3543	1	4	yes	direct product factor
517	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂×C₇	C₂²×H(5,𝔽₂)	1	2	yes	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	16	no	—
522	C₂³	—	2	8	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	16	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	32	no	—
528	C₂³	—	4	32	no	—
529	C₂³	—	4	32	no	—
530	C₂³	—	4	16	no	—
531	C₂³	—	8	32	no	—
532	C₂³	—	8	32	no	—
533	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
534	C₂³	C₂⁵×C₇	1	8	yes	—
535	C₂³	C₂⁵×C₇	1	8	yes	—
536	C₂³	C₂⁵×C₇	1	8	yes	—
537	C₂³	C₂⁵×C₇	1	2	yes	—
538	C₂³	C₂⁵×C₇	1	1	yes	characteristic
539	Q₈	—	2	16	no	—
540	D₄	—	2	32	no	—
541	D₄	—	2	16	no	—
542	D₄	—	2	32	no	—
543	D₄	—	2	32	no	—
544	D₄	—	4	32	no	—
545	D₄	—	4	32	no	—
546	D₄	—	4	8	no	—
547	D₄	—	4	16	no	—
548	D₄	—	4	8	no	—
549	D₄	—	4	32	no	—
550	D₄	—	4	32	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	16	no	—
559	C₂×C₄	—	2	32	no	—
560	C₂×C₄	—	4	16	no	—
561	C₂×C₄	—	4	32	no	—
562	C₂×C₄	C₇×H(5,𝔽₂)	1	8	yes	—
563	C₂×C₄	C₂⁵×C₇	1	2	yes	—
564	C₂×C₄	C₂⁵×C₇	1	4	yes	—
565	C₂×C₄	C₂⁵×C₇	1	2	yes	—
566	C₂×C₄	C₂⁵×C₇	1	8	yes	—
567	C₂×C₄	C₂⁵×C₇	1	8	yes	—
568	C₂×C₄	C₂⁵×C₇	1	8	yes	—
569	C₂×C₄	C₂⁵×C₇	1	4	yes	—
570	C₇	C₂×#3543	1	1	yes	characteristic, direct product factor, Sylow
571	C₂²	—	2	4	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	16	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	2	16	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	4	16	no	—
581	C₂²	—	4	16	no	—
582	C₂²	—	4	16	no	—
583	C₂²	—	8	32	no	—
584	C₂²	—	8	32	no	—
585	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
586	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
587	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
588	C₂²	C₂⁶×C₇	1	1	yes	characteristic
589	C₄	—	2	8	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	8	no	—
595	C₄	C₂×C₇×H(5,𝔽₂)	1	8	yes	—
596	C₂	—	2	4	no	—
597	C₂	—	4	8	no	—
598	C₂	—	4	8	no	—
599	C₂	—	4	8	no	—
600	C₂	C₇×#3543	1	4	yes	direct product factor
601	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂	C₂²×C₇×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#3543	C₂	direct (N × H)
2. C₂×C₇×#560	C₂	semidirect
3. C₂×C₇×#559	C₂	semidirect
4. C₂×C₇×#550	C₂	semidirect
5. C₂×C₇×#546	C₂	semidirect
6. C₂×C₇×D₄²	C₂	semidirect
7. C₂×C₇×D₄²	C₂	semidirect
8. C₂×C₇×#540	C₂	semidirect
9. C₂×C₇×#535	C₂	semidirect
10. C₂×C₇×#534	C₂	semidirect
11. C₂²×C₇×#127	C₂	semidirect
12. C₂×C₇×#529	C₂	semidirect
13. C₂²×C₇×#41	C₂²	semidirect
14. C₂³×C₇×D₄	C₂²	semidirect
15. C₂³×C₇×D₄	C₂²	semidirect
16. C₂³×C₇×D₄	C₂²	semidirect
17. C₂³×C₇×D₄	C₂²	semidirect
18. C₇×#560	C₂²	semidirect
19. C₇×#559	C₂²	semidirect
20. C₇×#550	C₂²	semidirect
21. C₇×#546	C₂²	semidirect
22. C₇×D₄²	C₂²	semidirect
23. C₇×D₄²	C₂²	semidirect
24. C₇×#540	C₂²	semidirect
25. C₇×#535	C₂²	semidirect
26. C₇×#534	C₂²	semidirect
28. C₂×C₇×#127	C₂²	semidirect
29. C₂×C₇×#127	C₂²	semidirect
30. C₂×C₇×#127	C₂²	semidirect
31. C₂×C₇×#127	C₂²	semidirect
32. C₂×C₇×#127	C₂²	semidirect
33. C₇×#529	C₂²	semidirect
34. C₂×C₇×#126	C₂²	semidirect
35. C₂×C₇×#125	C₂²	semidirect
36. C₂×C₇×#124	C₂²	semidirect
37. C₂×C₇×#124	C₂²	semidirect
38. C₂×C₇×#123	C₂²	semidirect
39. C₂×C₇×#123	C₂²	semidirect
40. C₂×C₇×#123	C₂²	semidirect
41. C₂×C₇×#123	C₂²	semidirect
42. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₇×#121	C₂²	semidirect
45. C₂×C₇×#121	C₂²	semidirect
46. C₂×C₇×#121	C₂²	semidirect
47. C₂×C₇×#121	C₂²	semidirect
48. C₂×C₇×#121	C₂²	semidirect
49. C₂×C₇×#121	C₂²	semidirect
50. C₂×C₇×#120	C₂²	semidirect
51. C₂×C₇×#120	C₂²	semidirect
52. C₂×C₇×#120	C₂²	semidirect
53. C₂×C₇×#120	C₂²	semidirect
54. C₂×C₄×C₇×Q₈	C₂²	semidirect
55. C₂×C₄×C₇×D₄	C₂²	semidirect
56. C₂×C₄×C₇×D₄	C₂²	semidirect
57. C₂×C₄×C₇×D₄	C₂²	semidirect
58. C₂×C₄×C₇×D₄	C₂²	semidirect
59. C₂×C₇×#117	C₂²	semidirect
60. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
61. C₂²×C₄²×C₇	C₂²	semidirect
62. C₂×#3543	C₇	direct (N × H)
66. C₂×C₇×#41	C₂³	semidirect
83. C₂²×C₇×D₄	C₂³	semidirect
84. C₂²×C₇×D₄	C₂³	semidirect
85. C₂²×C₇×D₄	C₂³	semidirect
86. C₂²×C₇×D₄	C₂³	semidirect
93. C₇×#127	C₂³	semidirect
94. C₇×#127	C₂³	semidirect
95. C₇×#127	C₂³	semidirect
96. C₇×#127	C₂³	semidirect
97. C₇×#126	C₂³	semidirect
98. C₇×#125	C₂³	semidirect
99. C₇×#124	C₂³	semidirect
100. C₇×#124	C₂³	semidirect
101. C₇×#123	C₂³	semidirect
102. C₇×#123	C₂³	semidirect
103. C₇×#123	C₂³	semidirect
104. C₇×#123	C₂³	semidirect
105. C₇×C₂²⋊Q₈	C₂³	semidirect
107. C₇×#121	C₂³	semidirect
108. C₇×#121	C₂³	semidirect
109. C₇×#121	C₂³	semidirect
110. C₇×#121	C₂³	semidirect
111. C₇×#121	C₂³	semidirect
112. C₇×#121	C₂³	semidirect
113. C₇×#120	C₂³	semidirect
114. C₇×#120	C₂³	semidirect
115. C₇×#120	C₂³	semidirect
116. C₇×#120	C₂³	semidirect
117. C₄×C₇×Q₈	C₂³	semidirect
118. C₄×C₇×D₄	C₂³	semidirect
119. C₄×C₇×D₄	C₂³	semidirect
120. C₄×C₇×D₄	C₂³	semidirect
121. C₄×C₇×D₄	C₂³	semidirect
122. C₇×#117	C₂³	semidirect
138. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
143. C₂×C₄²×C₇	C₂³	semidirect
144. #3543	C₂×C₇	direct (N × H)
145. C₂×#560	C₂×C₇	semidirect
146. C₂×#559	C₂×C₇	semidirect
147. C₂×#550	C₂×C₇	semidirect
148. C₂×#546	C₂×C₇	semidirect
149. C₂×D₄²	C₂×C₇	semidirect
150. C₂×D₄²	C₂×C₇	semidirect
151. C₂×#540	C₂×C₇	semidirect
152. C₂×#535	C₂×C₇	semidirect
153. C₂×#534	C₂×C₇	semidirect
154. C₂²×#127	C₂×C₇	semidirect
155. C₂×#529	C₂×C₇	semidirect
231. C₂²×#41	C₂²×C₇	semidirect
232. C₂³×D₄	C₂²×C₇	semidirect
233. C₂³×D₄	C₂²×C₇	semidirect
234. C₂³×D₄	C₂²×C₇	semidirect
235. C₂³×D₄	C₂²×C₇	semidirect
236. #560	C₂²×C₇	semidirect
237. #559	C₂²×C₇	semidirect
238. #550	C₂²×C₇	semidirect
239. #546	C₂²×C₇	semidirect
240. D₄²	C₂²×C₇	semidirect
241. D₄²	C₂²×C₇	semidirect
242. #540	C₂²×C₇	semidirect
243. #535	C₂²×C₇	semidirect
244. #534	C₂²×C₇	semidirect
246. C₂×#127	C₂²×C₇	semidirect
247. C₂×#127	C₂²×C₇	semidirect
248. C₂×#127	C₂²×C₇	semidirect
249. C₂×#127	C₂²×C₇	semidirect
250. C₂×#127	C₂²×C₇	semidirect
251. #529	C₂²×C₇	semidirect
252. C₂×#126	C₂²×C₇	semidirect
253. C₂×#125	C₂²×C₇	semidirect
254. C₂×#124	C₂²×C₇	semidirect
255. C₂×#124	C₂²×C₇	semidirect
256. C₂×#123	C₂²×C₇	semidirect
257. C₂×#123	C₂²×C₇	semidirect
258. C₂×#123	C₂²×C₇	semidirect
259. C₂×#123	C₂²×C₇	semidirect
260. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
262. C₂×#121	C₂²×C₇	semidirect
263. C₂×#121	C₂²×C₇	semidirect
264. C₂×#121	C₂²×C₇	semidirect
265. C₂×#121	C₂²×C₇	semidirect
266. C₂×#121	C₂²×C₇	semidirect
267. C₂×#121	C₂²×C₇	semidirect
268. C₂×#120	C₂²×C₇	semidirect
269. C₂×#120	C₂²×C₇	semidirect
270. C₂×#120	C₂²×C₇	semidirect
271. C₂×#120	C₂²×C₇	semidirect
272. C₂×C₄×Q₈	C₂²×C₇	semidirect
273. C₂×C₄×D₄	C₂²×C₇	semidirect
274. C₂×C₄×D₄	C₂²×C₇	semidirect
275. C₂×C₄×D₄	C₂²×C₇	semidirect
276. C₂×C₄×D₄	C₂²×C₇	semidirect
277. C₂×#117	C₂²×C₇	semidirect
278. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
279. C₂²×C₄²	C₂²×C₇	semidirect
334. C₂×#41	C₂³×C₇	semidirect
351. C₂²×D₄	C₂³×C₇	semidirect
352. C₂²×D₄	C₂³×C₇	semidirect
353. C₂²×D₄	C₂³×C₇	semidirect
354. C₂²×D₄	C₂³×C₇	semidirect
361. #127	C₂³×C₇	semidirect
362. #127	C₂³×C₇	semidirect
363. #127	C₂³×C₇	semidirect
364. #127	C₂³×C₇	semidirect
365. #126	C₂³×C₇	semidirect
366. #125	C₂³×C₇	semidirect
367. #124	C₂³×C₇	semidirect
368. #124	C₂³×C₇	semidirect
369. #123	C₂³×C₇	semidirect
370. #123	C₂³×C₇	semidirect
371. #123	C₂³×C₇	semidirect
372. #123	C₂³×C₇	semidirect
373. C₂²⋊Q₈	C₂³×C₇	semidirect
375. #121	C₂³×C₇	semidirect
376. #121	C₂³×C₇	semidirect
377. #121	C₂³×C₇	semidirect
378. #121	C₂³×C₇	semidirect
379. #121	C₂³×C₇	semidirect
380. #121	C₂³×C₇	semidirect
381. #120	C₂³×C₇	semidirect
382. #120	C₂³×C₇	semidirect
383. #120	C₂³×C₇	semidirect
384. #120	C₂³×C₇	semidirect
385. C₄×Q₈	C₂³×C₇	semidirect
386. C₄×D₄	C₂³×C₇	semidirect
387. C₄×D₄	C₂³×C₇	semidirect
388. C₄×D₄	C₂³×C₇	semidirect
389. C₄×D₄	C₂³×C₇	semidirect
390. #117	C₂³×C₇	semidirect
406. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
411. C₂×C₄²	C₂³×C₇	semidirect
516. C₂×C₇	#3543	direct (N × H)
570. C₇	C₂×#3543	direct (N × H)
600. C₂	C₇×#3543	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×#3543	2
C₂×C₇×#560	2
C₂×C₇×#559	2
C₂×C₇×#550	2
C₂×C₇×#546	2
C₂×C₇×D₄²	2
C₂×C₇×#540	2
C₂×C₇×#535	2
C₂×C₇×#534	2
C₂²×C₇×#127	2
C₂×C₇×#529	2
C₂×#3543	7

Subgroups — C2×C7×#3543 #13239960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3543 #13239960