Subgroups — C₂×C₇×#3179 #13237900

Order 1792.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3179	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
20	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#542	—	2	4	no	—
24	C₇×#542	C₂²	1	8	yes	complemented
25	C₇×#540	—	2	4	no	—
26	C₇×#540	C₂²	1	8	yes	complemented
27	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×#127	C₂²	1	1	yes	characteristic
29	C₂×C₇×#126	—	2	1	no	—
30	C₂×C₇×#125	C₂²	1	1	yes	characteristic
31	C₂×C₇×#124	—	2	1	no	—
32	C₂×C₇×#124	C₂²	1	1	yes	characteristic
33	C₂×C₇×#123	—	2	1	no	—
34	C₂×C₇×#123	—	2	1	no	—
35	C₂×C₇×#123	—	2	1	no	—
36	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
37	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×#121	—	2	1	no	—
39	C₂×C₇×#121	—	2	1	no	—
40	C₂×C₇×#121	C₂²	1	1	yes	characteristic
41	C₂×C₇×#121	C₂²	1	1	yes	characteristic
42	C₂×C₇×#121	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₇×#117	C₂²	1	1	yes	characteristic
48	C₇×#501	C₂²	1	8	yes	complemented
49	C₇×#496	C₂²	1	8	yes	complemented
50	C₇×#488	C₂²	1	8	yes	complemented
51	C₇×#486	C₂²	1	8	yes	complemented
52	C₇×#469	C₂²	1	8	yes	complemented
53	C₇×#468	C₂²	1	8	yes	complemented
54	C₇×#466	C₂²	1	8	yes	complemented
55	C₇×#465	C₂²	1	8	yes	complemented
56	C₇×#442	C₂²	1	8	yes	complemented
57	C₇×#440	C₂²	1	8	yes	complemented
58	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
59	C₄×C₇×D₈	C₂²	1	8	yes	complemented
60	C₂×C₇×#107	C₂²	1	1	yes	characteristic
61	C₂×C₇×#107	C₂²	1	1	yes	characteristic
62	C₂×C₇×#106	C₂²	1	1	yes	characteristic
63	C₂×C₇×#106	C₂²	1	1	yes	characteristic
64	C₂×C₇×#103	C₂²	1	1	yes	characteristic
65	C₂×C₇×#103	C₂²	1	1	yes	characteristic
66	C₂×C₇×#102	C₂²	1	1	yes	characteristic
67	C₂×C₇×#102	C₂²	1	1	yes	characteristic
68	C₂×C₇×#102	C₂²	1	1	yes	characteristic
69	C₂×C₇×#102	C₂²	1	1	yes	characteristic
70	C₂×C₇×#102	C₂²	1	1	yes	characteristic
71	C₂×C₇×#102	C₂²	1	1	yes	characteristic
72	C₇×#405	C₂²	1	8	yes	complemented
73	C₂×C₇×#97	C₂²	1	1	yes	characteristic
74	C₂×C₇×#97	C₂²	1	1	yes	characteristic
75	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
77	C₂×#3179	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂²×C₇×Q₈	—	2	1	no	—
79	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×D₄	—	2	1	no	—
81	C₂²×C₇×D₄	—	2	1	no	—
82	C₂²×C₇×D₄	—	2	1	no	—
83	C₂²×C₇×D₄	—	2	1	no	—
84	C₂²×C₇×D₄	—	2	1	no	—
85	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
86	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
87	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇	—	2	1	no	—
89	C₂³×C₄×C₇	—	2	1	no	—
90	C₂³×C₄×C₇	—	2	1	no	—
91	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
92	C₂×C₇×SD₁₆	—	2	4	no	—
93	C₂×C₇×SD₁₆	—	2	4	no	—
94	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
95	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
96	C₂×C₇×D₈	—	2	4	no	—
97	C₂×C₇×D₈	—	2	4	no	—
98	C₂×C₇×D₈	C₂³	1	4	yes	—
99	C₂×C₇×D₈	C₂³	1	4	yes	—
100	C₂×C₇×M₁₆	—	2	4	no	—
101	C₂×C₇×M₁₆	C₂³	1	4	yes	—
102	C₂²×C₇×C₈	—	2	4	no	—
103	C₂²×C₇×C₈	C₂³	1	4	yes	—
104	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₇×#127	—	2	2	no	—
111	C₇×#127	C₂³	1	4	yes	—
112	C₇×#126	—	2	8	no	—
113	C₇×#125	—	2	2	no	—
114	C₇×#125	C₂³	1	4	yes	—
115	C₇×#124	—	2	8	no	—
116	C₇×#124	—	2	2	no	—
117	C₇×#124	C₂³	1	4	yes	—
118	C₇×#123	—	2	8	no	—
119	C₇×#123	—	2	8	no	—
120	C₇×#123	—	2	8	no	—
121	C₇×C₂²⋊Q₈	—	2	2	no	—
122	C₇×C₂²⋊Q₈	—	2	8	no	—
123	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₇×#121	—	2	2	no	—
125	C₇×#121	—	2	2	no	—
126	C₇×#121	—	2	2	no	—
127	C₇×#121	—	2	8	no	—
128	C₇×#121	—	2	8	no	—
129	C₇×#121	C₂³	1	4	yes	—
130	C₇×#121	C₂³	1	4	yes	—
131	C₇×#121	C₂³	1	4	yes	—
132	C₄×C₇×Q₈	—	2	2	no	—
133	C₄×C₇×Q₈	C₂³	1	4	yes	—
134	C₄×C₇×D₄	—	2	2	no	—
135	C₄×C₇×D₄	—	2	2	no	—
136	C₄×C₇×D₄	—	2	2	no	—
137	C₄×C₇×D₄	C₂³	1	4	yes	—
138	C₄×C₇×D₄	C₂³	1	4	yes	—
139	C₄×C₇×D₄	C₂³	1	4	yes	—
140	C₇×#117	D₄	1	4	yes	—
141	C₇×#117	C₂³	1	4	yes	—
142	C₂×C₇×C₄⋊C₄	—	2	1	no	—
143	C₂×C₇×C₄⋊C₄	—	2	1	no	—
144	C₂×C₇×C₄⋊C₄	—	2	1	no	—
145	C₂×C₇×C₄⋊C₄	—	2	1	no	—
146	C₂×C₇×C₄⋊C₄	—	2	1	no	—
147	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
163	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₇	—	2	1	no	—
165	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
167	C₇×#107	C₂³	1	4	yes	—
168	C₇×#107	C₂³	1	4	yes	—
169	C₇×#106	C₂³	1	4	yes	—
170	C₇×#106	C₂³	1	4	yes	—
171	C₇×#103	C₂³	1	4	yes	—
172	C₇×#103	C₂³	1	4	yes	—
173	C₇×#102	C₂³	1	4	yes	—
174	C₇×#102	C₂³	1	4	yes	—
175	C₇×#102	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	4	yes	—
177	C₇×#102	C₂³	1	4	yes	—
178	C₇×#102	C₂³	1	4	yes	—
179	C₇×#97	C₂³	1	4	yes	—
180	C₇×#97	C₂³	1	4	yes	—
181	C₄×C₇×C₈	C₂³	1	4	yes	—
182	C₄×C₇×C₈	C₂³	1	4	yes	—
183	C₂×#542	C₂×C₇	1	1	yes	characteristic, complemented
184	C₂×#540	C₂×C₇	1	1	yes	characteristic, complemented
185	#3179	C₂×C₇	1	16	yes	direct product factor
186	C₂×#501	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#496	C₂×C₇	1	1	yes	characteristic, complemented
188	C₂×#488	C₂×C₇	1	1	yes	characteristic, complemented
189	C₂×#486	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#469	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#468	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#465	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂⁴×C₇	—	2	1	no	—
200	C₂⁴×C₇	—	2	1	no	—
201	C₂⁴×C₇	—	2	1	no	—
202	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
203	C₂×C₇×Q₈	—	2	1	no	—
204	C₂×C₇×Q₈	—	2	4	no	—
205	C₂×C₇×Q₈	—	2	2	no	—
206	C₂×C₇×Q₈	—	2	2	no	—
207	C₂×C₇×Q₈	—	8	2	no	—
208	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
209	C₂×C₇×D₄	—	2	4	no	—
210	C₂×C₇×D₄	—	2	4	no	—
211	C₂×C₇×D₄	—	2	4	no	—
212	C₂×C₇×D₄	—	2	1	no	—
213	C₂×C₇×D₄	—	2	1	no	—
214	C₂×C₇×D₄	—	2	1	no	—
215	C₂×C₇×D₄	—	2	4	no	—
216	C₂×C₇×D₄	—	2	4	no	—
217	C₂×C₇×D₄	—	2	2	no	—
218	C₂×C₇×D₄	—	2	2	no	—
219	C₂×C₇×D₄	—	2	2	no	—
220	C₂×C₇×D₄	—	2	2	no	—
221	C₂×C₇×D₄	—	2	2	no	—
222	C₂×C₇×D₄	—	2	2	no	—
223	C₂×C₇×D₄	—	8	2	no	—
224	C₂×C₇×D₄	—	8	2	no	—
225	C₂×C₇×D₄	—	8	2	no	—
226	C₂×C₇×D₄	—	8	2	no	—
227	C₂×C₇×D₄	—	8	2	no	—
228	C₂×C₇×D₄	C₂⁴	1	2	yes	—
229	C₂×C₇×D₄	C₂⁴	1	2	yes	—
230	C₂×C₇×D₄	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₇	—	2	2	no	—
232	C₂²×C₄×C₇	—	2	2	no	—
233	C₂²×C₄×C₇	—	2	1	no	—
234	C₂²×C₄×C₇	—	2	1	no	—
235	C₂²×C₄×C₇	—	2	1	no	—
236	C₂²×C₄×C₇	—	2	1	no	—
237	C₂²×C₄×C₇	—	2	1	no	—
238	C₂²×C₄×C₇	—	2	4	no	—
239	C₂²×C₄×C₇	—	2	4	no	—
240	C₂²×C₄×C₇	—	2	4	no	—
241	C₂²×C₄×C₇	—	8	2	no	—
242	C₂²×C₄×C₇	—	8	2	no	—
243	C₂²×C₄×C₇	—	8	2	no	—
244	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
245	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
252	C₇×SD₁₆	—	2	8	no	—
253	C₇×SD₁₆	—	2	8	no	—
254	C₇×D₈	—	2	8	no	—
255	C₇×D₈	—	2	8	no	—
256	C₇×M₁₆	—	2	8	no	—
257	C₂×C₇×C₈	—	2	2	no	—
258	C₂×C₇×C₈	—	2	2	no	—
259	C₂×C₇×C₈	—	2	8	no	—
260	C₂×C₇×C₈	#41	1	4	yes	—
261	C₂×C₇×C₈	#41	1	4	yes	—
262	C₂×C₇×C₈	C₂⁴	1	2	yes	—
263	C₂×C₇×C₈	C₂⁴	1	2	yes	—
264	C₂×C₇×C₈	C₂⁴	1	2	yes	—
265	C₂×C₇×C₈	C₂⁴	1	2	yes	—
266	C₇×C₄⋊C₄	—	2	4	no	—
267	C₇×C₄⋊C₄	—	2	4	no	—
268	C₇×C₄⋊C₄	—	2	4	no	—
269	C₇×C₄⋊C₄	—	2	4	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	—	2	1	no	—
272	C₇×C₄⋊C₄	—	2	1	no	—
273	C₇×C₄⋊C₄	—	2	1	no	—
274	C₇×C₄⋊C₄	—	2	1	no	—
275	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
276	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₇×C₂²⋊C₄	—	2	4	no	—
282	C₇×C₂²⋊C₄	—	2	4	no	—
283	C₇×C₂²⋊C₄	—	2	4	no	—
284	C₇×C₂²⋊C₄	—	2	4	no	—
285	C₇×C₂²⋊C₄	—	2	4	no	—
286	C₇×C₂²⋊C₄	—	2	4	no	—
287	C₇×C₂²⋊C₄	—	2	4	no	—
288	C₇×C₂²⋊C₄	—	2	4	no	—
289	C₇×C₂²⋊C₄	—	2	4	no	—
290	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
291	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
292	C₄²×C₇	—	2	4	no	—
293	C₄²×C₇	C₂×D₄	1	2	yes	—
294	C₄²×C₇	C₂×D₄	1	2	yes	—
295	C₄²×C₇	C₂⁴	1	2	yes	—
296	C₄²×C₇	C₂⁴	1	2	yes	—
297	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
298	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
299	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
300	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
301	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
302	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
303	#542	—	2	4	no	—
304	#542	C₂²×C₇	1	8	yes	complemented
305	#540	—	2	4	no	—
306	#540	C₂²×C₇	1	8	yes	complemented
307	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
308	C₂×#127	C₂²×C₇	1	1	yes	characteristic
309	C₂×#126	—	2	1	no	—
310	C₂×#125	C₂²×C₇	1	1	yes	characteristic
311	C₂×#124	—	2	1	no	—
312	C₂×#124	C₂²×C₇	1	1	yes	characteristic
313	C₂×#123	—	2	1	no	—
314	C₂×#123	—	2	1	no	—
315	C₂×#123	—	2	1	no	—
316	C₂×C₂²⋊Q₈	—	2	1	no	—
317	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
318	C₂×#121	—	2	1	no	—
319	C₂×#121	—	2	1	no	—
320	C₂×#121	C₂²×C₇	1	1	yes	characteristic
321	C₂×#121	C₂²×C₇	1	1	yes	characteristic
322	C₂×#121	C₂²×C₇	1	1	yes	characteristic
323	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
325	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
326	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
327	C₂×#117	C₂²×C₇	1	1	yes	characteristic
328	#501	C₂²×C₇	1	8	yes	complemented
329	#496	C₂²×C₇	1	8	yes	complemented
330	#488	C₂²×C₇	1	8	yes	complemented
331	#486	C₂²×C₇	1	8	yes	complemented
332	#469	C₂²×C₇	1	8	yes	complemented
333	#468	C₂²×C₇	1	8	yes	complemented
334	#466	C₂²×C₇	1	8	yes	complemented
335	#465	C₂²×C₇	1	8	yes	complemented
336	#442	C₂²×C₇	1	8	yes	complemented
337	#440	C₂²×C₇	1	8	yes	complemented
338	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
339	C₄×D₈	C₂²×C₇	1	8	yes	complemented
340	C₂×#107	C₂²×C₇	1	1	yes	characteristic
341	C₂×#107	C₂²×C₇	1	1	yes	characteristic
342	C₂×#106	C₂²×C₇	1	1	yes	characteristic
343	C₂×#106	C₂²×C₇	1	1	yes	characteristic
344	C₂×#103	C₂²×C₇	1	1	yes	characteristic
345	C₂×#103	C₂²×C₇	1	1	yes	characteristic
346	C₂×#102	C₂²×C₇	1	1	yes	characteristic
347	C₂×#102	C₂²×C₇	1	1	yes	characteristic
348	C₂×#102	C₂²×C₇	1	1	yes	characteristic
349	C₂×#102	C₂²×C₇	1	1	yes	characteristic
350	C₂×#102	C₂²×C₇	1	1	yes	characteristic
351	C₂×#102	C₂²×C₇	1	1	yes	characteristic
352	#405	C₂²×C₇	1	8	yes	complemented
353	C₂×#97	C₂²×C₇	1	1	yes	characteristic
354	C₂×#97	C₂²×C₇	1	1	yes	characteristic
355	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
356	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
357	C₂³×C₇	—	2	2	no	—
358	C₂³×C₇	—	2	2	no	—
359	C₂³×C₇	—	2	2	no	—
360	C₂³×C₇	—	2	2	no	—
361	C₂³×C₇	—	2	2	no	—
362	C₂³×C₇	—	2	2	no	—
363	C₂³×C₇	—	4	2	no	—
364	C₂³×C₇	—	4	2	no	—
365	C₂³×C₇	—	4	2	no	—
366	C₂³×C₇	—	4	2	no	—
367	C₂³×C₇	—	4	2	no	—
368	C₂³×C₇	—	4	2	no	—
369	C₂³×C₇	—	4	2	no	—
370	C₂³×C₇	—	4	2	no	—
371	C₂³×C₇	—	4	2	no	—
372	C₂³×C₇	C₂²×D₄	1	2	yes	—
373	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
374	C₇×Q₈	—	2	2	no	—
375	C₇×Q₈	—	2	2	no	—
376	C₇×Q₈	—	4	2	no	—
377	C₇×Q₈	—	8	4	no	—
378	C₇×D₄	—	2	2	no	—
379	C₇×D₄	—	2	2	no	—
380	C₇×D₄	—	2	2	no	—
381	C₇×D₄	—	2	2	no	—
382	C₇×D₄	—	2	2	no	—
383	C₇×D₄	—	2	2	no	—
384	C₇×D₄	—	4	2	no	—
385	C₇×D₄	—	4	2	no	—
386	C₇×D₄	—	4	2	no	—
387	C₇×D₄	—	8	4	no	—
388	C₇×D₄	—	8	4	no	—
389	C₇×D₄	—	8	4	no	—
390	C₇×D₄	—	8	4	no	—
391	C₇×D₄	—	8	4	no	—
392	C₂×C₄×C₇	—	2	2	no	—
393	C₂×C₄×C₇	—	2	2	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	2	2	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	4	no	—
398	C₂×C₄×C₇	—	2	2	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	2	2	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	4	2	no	—
406	C₂×C₄×C₇	—	4	2	no	—
407	C₂×C₄×C₇	—	4	2	no	—
408	C₂×C₄×C₇	—	4	2	no	—
409	C₂×C₄×C₇	—	4	2	no	—
410	C₂×C₄×C₇	—	8	4	no	—
411	C₂×C₄×C₇	—	8	4	no	—
412	C₂×C₄×C₇	—	8	4	no	—
413	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₇	C₂×#41	1	2	yes	—
420	C₂×C₄×C₇	C₂×#41	1	2	yes	—
421	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
422	C₇×C₈	—	2	2	no	—
423	C₇×C₈	—	2	2	no	—
424	C₇×C₈	C₂×#41	1	4	yes	—
425	C₇×C₈	C₂×#41	1	4	yes	—
426	C₂²×Q₈	—	2	1	no	—
427	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
428	C₂²×D₄	—	2	1	no	—
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
434	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
435	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
440	C₂×SD₁₆	—	2	4	no	—
441	C₂×SD₁₆	—	2	4	no	—
442	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
443	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
444	C₂×D₈	—	2	4	no	—
445	C₂×D₈	—	2	4	no	—
446	C₂×D₈	C₂³×C₇	1	4	yes	—
447	C₂×D₈	C₂³×C₇	1	4	yes	—
448	C₂×M₁₆	—	2	4	no	—
449	C₂×M₁₆	C₂³×C₇	1	4	yes	—
450	C₂²×C₈	—	2	4	no	—
451	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₇	1	4	yes	—
453	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
458	#127	—	2	2	no	—
459	#127	C₂³×C₇	1	4	yes	—
460	#126	—	2	8	no	—
461	#125	—	2	2	no	—
462	#125	C₂³×C₇	1	4	yes	—
463	#124	—	2	8	no	—
464	#124	—	2	2	no	—
465	#124	C₂³×C₇	1	4	yes	—
466	#123	—	2	8	no	—
467	#123	—	2	8	no	—
468	#123	—	2	8	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	8	no	—
471	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	8	no	—
476	#121	—	2	8	no	—
477	#121	C₂³×C₇	1	4	yes	—
478	#121	C₂³×C₇	1	4	yes	—
479	#121	C₂³×C₇	1	4	yes	—
480	C₄×Q₈	—	2	2	no	—
481	C₄×Q₈	C₂³×C₇	1	4	yes	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	C₂³×C₇	1	4	yes	—
486	C₄×D₄	C₂³×C₇	1	4	yes	—
487	C₄×D₄	C₂³×C₇	1	4	yes	—
488	#117	C₇×D₄	1	4	yes	—
489	#117	C₂³×C₇	1	4	yes	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
512	C₂×C₄²	—	2	1	no	—
513	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
515	#107	C₂³×C₇	1	4	yes	—
516	#107	C₂³×C₇	1	4	yes	—
517	#106	C₂³×C₇	1	4	yes	—
518	#106	C₂³×C₇	1	4	yes	—
519	#103	C₂³×C₇	1	4	yes	—
520	#103	C₂³×C₇	1	4	yes	—
521	#102	C₂³×C₇	1	4	yes	—
522	#102	C₂³×C₇	1	4	yes	—
523	#102	C₂³×C₇	1	4	yes	—
524	#102	C₂³×C₇	1	4	yes	—
525	#102	C₂³×C₇	1	4	yes	—
526	#102	C₂³×C₇	1	4	yes	—
527	#97	C₂³×C₇	1	4	yes	—
528	#97	C₂³×C₇	1	4	yes	—
529	C₄×C₈	C₂³×C₇	1	4	yes	—
530	C₄×C₈	C₂³×C₇	1	4	yes	—
531	C₂²×C₇	—	2	2	no	—
532	C₂²×C₇	—	2	2	no	—
533	C₂²×C₇	—	2	2	no	—
534	C₂²×C₇	—	4	4	no	—
535	C₂²×C₇	—	4	2	no	—
536	C₂²×C₇	—	4	2	no	—
537	C₂²×C₇	—	4	2	no	—
538	C₂²×C₇	—	4	2	no	—
539	C₂²×C₇	—	4	2	no	—
540	C₂²×C₇	—	4	2	no	—
541	C₂²×C₇	—	4	2	no	—
542	C₂²×C₇	—	4	2	no	—
543	C₂²×C₇	—	4	2	no	—
544	C₂²×C₇	—	8	4	no	—
545	C₂²×C₇	—	8	4	no	—
546	C₂²×C₇	—	8	4	no	—
547	C₂²×C₇	#532	1	2	yes	—
548	C₂²×C₇	#576	1	2	yes	—
549	C₂²×C₇	#577	1	2	yes	—
550	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₇	—	2	2	no	—
552	C₄×C₇	—	2	2	no	—
553	C₄×C₇	—	2	2	no	—
554	C₄×C₇	—	2	2	no	—
555	C₄×C₇	—	2	2	no	—
556	C₄×C₇	—	4	2	no	—
557	C₄×C₇	—	4	2	no	—
558	C₄×C₇	—	4	2	no	—
559	C₄×C₇	—	4	2	no	—
560	C₄×C₇	—	4	2	no	—
561	C₄×C₇	#532	1	2	yes	—
562	C₄×C₇	C₂²×#41	1	1	yes	characteristic
563	C₄×C₇	C₂²×#41	1	1	yes	characteristic
564	C₂⁴	—	2	1	no	—
565	C₂⁴	—	2	1	no	—
566	C₂⁴	—	2	1	no	—
567	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	8	2	no	—
573	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	8	2	no	—
589	C₂×D₄	—	8	2	no	—
590	C₂×D₄	—	8	2	no	—
591	C₂×D₄	—	8	2	no	—
592	C₂×D₄	—	8	2	no	—
593	C₂×D₄	C₂⁴×C₇	1	2	yes	—
594	C₂×D₄	C₂⁴×C₇	1	2	yes	—
595	C₂×D₄	C₂⁴×C₇	1	2	yes	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	8	2	no	—
607	C₂²×C₄	—	8	2	no	—
608	C₂²×C₄	—	8	2	no	—
609	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
610	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
611	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
612	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
613	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
614	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
617	SD₁₆	—	2	8	no	—
618	SD₁₆	—	2	8	no	—
619	D₈	—	2	8	no	—
620	D₈	—	2	8	no	—
621	M₁₆	—	2	8	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	8	no	—
625	C₂×C₈	C₇×#41	1	4	yes	—
626	C₂×C₈	C₇×#41	1	4	yes	—
627	C₂×C₈	C₂⁴×C₇	1	2	yes	—
628	C₂×C₈	C₂⁴×C₇	1	2	yes	—
629	C₂×C₈	C₂⁴×C₇	1	2	yes	—
630	C₂×C₈	C₂⁴×C₇	1	2	yes	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
641	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
642	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
656	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	C₂×C₇×D₄	1	2	yes	—
659	C₄²	C₂×C₇×D₄	1	2	yes	—
660	C₄²	C₂⁴×C₇	1	2	yes	—
661	C₄²	C₂⁴×C₇	1	2	yes	—
662	C₂×C₇	—	4	2	no	—
663	C₂×C₇	—	8	2	no	—
664	C₂×C₇	—	8	2	no	—
665	C₂×C₇	—	8	2	no	—
666	C₂×C₇	#3179	1	4	yes	direct product factor
667	C₂×C₇	C₂×#532	1	1	yes	characteristic
668	C₂×C₇	C₂×#576	1	1	yes	characteristic
669	C₂×C₇	C₂×#577	1	1	yes	characteristic
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	4	2	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	C₂²×C₇×D₄	1	2	yes	—
686	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
687	Q₈	—	2	2	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	4	2	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
727	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
728	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
729	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
730	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
731	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
732	C₂×C₄	C₂×C₇×#41	1	2	yes	—
733	C₂×C₄	C₂×C₇×#41	1	2	yes	—
734	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
735	C₈	—	2	2	no	—
736	C₈	—	2	2	no	—
737	C₈	C₂×C₇×#41	1	4	yes	—
738	C₈	C₂×C₇×#41	1	4	yes	—
739	C₇	C₂×#3179	1	1	yes	characteristic, direct product factor, Sylow
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	8	4	no	—
754	C₂²	—	8	4	no	—
755	C₂²	—	8	4	no	—
756	C₂²	C₇×#532	1	2	yes	—
757	C₂²	C₇×#576	1	2	yes	—
758	C₂²	C₇×#577	1	2	yes	—
759	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	C₇×#532	1	2	yes	—
771	C₄	C₂²×C₇×#41	1	1	yes	characteristic
772	C₄	C₂²×C₇×#41	1	1	yes	characteristic
773	C₂	—	4	2	no	—
774	C₂	—	8	2	no	—
775	C₂	—	8	2	no	—
776	C₂	—	8	2	no	—
777	C₂	C₇×#3179	1	4	yes	direct product factor
778	C₂	C₂×C₇×#532	1	1	yes	characteristic
779	C₂	C₂×C₇×#576	1	1	yes	characteristic
780	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#542	C₂	semidirect
2. C₂×C₇×#540	C₂	semidirect
3. C₇×#3179	C₂	direct (N × H)
4. C₂×C₇×#501	C₂	semidirect
5. C₂×C₇×#496	C₂	semidirect
6. C₂×C₇×#488	C₂	semidirect
7. C₂×C₇×#486	C₂	semidirect
8. C₂×C₇×#469	C₂	semidirect
9. C₂×C₇×#468	C₂	semidirect
10. C₂×C₇×#466	C₂	semidirect
11. C₂×C₇×#465	C₂	semidirect
12. C₂×C₇×#442	C₂	semidirect
13. C₂×C₇×#440	C₂	semidirect
14. C₂×C₄×C₇×SD₁₆	C₂	semidirect
15. C₂×C₄×C₇×D₈	C₂	semidirect
16. C₂×C₇×#405	C₂	semidirect
24. C₇×#542	C₂²	semidirect
26. C₇×#540	C₂²	semidirect
48. C₇×#501	C₂²	semidirect
49. C₇×#496	C₂²	semidirect
50. C₇×#488	C₂²	semidirect
51. C₇×#486	C₂²	semidirect
52. C₇×#469	C₂²	semidirect
53. C₇×#468	C₂²	semidirect
54. C₇×#466	C₂²	semidirect
55. C₇×#465	C₂²	semidirect
56. C₇×#442	C₂²	semidirect
57. C₇×#440	C₂²	semidirect
58. C₄×C₇×SD₁₆	C₂²	semidirect
59. C₄×C₇×D₈	C₂²	semidirect
72. C₇×#405	C₂²	semidirect
77. C₂×#3179	C₇	direct (N × H)
183. C₂×#542	C₂×C₇	semidirect
184. C₂×#540	C₂×C₇	semidirect
185. #3179	C₂×C₇	direct (N × H)
186. C₂×#501	C₂×C₇	semidirect
187. C₂×#496	C₂×C₇	semidirect
188. C₂×#488	C₂×C₇	semidirect
189. C₂×#486	C₂×C₇	semidirect
190. C₂×#469	C₂×C₇	semidirect
191. C₂×#468	C₂×C₇	semidirect
192. C₂×#466	C₂×C₇	semidirect
193. C₂×#465	C₂×C₇	semidirect
194. C₂×#442	C₂×C₇	semidirect
195. C₂×#440	C₂×C₇	semidirect
196. C₂×C₄×SD₁₆	C₂×C₇	semidirect
197. C₂×C₄×D₈	C₂×C₇	semidirect
198. C₂×#405	C₂×C₇	semidirect
304. #542	C₂²×C₇	semidirect
306. #540	C₂²×C₇	semidirect
328. #501	C₂²×C₇	semidirect
329. #496	C₂²×C₇	semidirect
330. #488	C₂²×C₇	semidirect
331. #486	C₂²×C₇	semidirect
332. #469	C₂²×C₇	semidirect
333. #468	C₂²×C₇	semidirect
334. #466	C₂²×C₇	semidirect
335. #465	C₂²×C₇	semidirect
336. #442	C₂²×C₇	semidirect
337. #440	C₂²×C₇	semidirect
338. C₄×SD₁₆	C₂²×C₇	semidirect
339. C₄×D₈	C₂²×C₇	semidirect
352. #405	C₂²×C₇	semidirect
666. C₂×C₇	#3179	direct (N × H)
739. C₇	C₂×#3179	direct (N × H)
777. C₂	C₇×#3179	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#542	2
C₂×C₇×#540	2
C₇×#3179	2
C₂×C₇×#501	2
C₂×C₇×#496	2
C₂×C₇×#488	2
C₂×C₇×#486	2
C₂×C₇×#469	2
C₂×C₇×#468	2
C₂×C₇×#466	2
C₂×C₇×#465	2
C₂×C₇×#442	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#405	2
C₂×#3179	7

Subgroups — C2×C7×#3179 #13237900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3179 #13237900