Subgroups — C₂×C₇×#3121 #13237766

Order 1792.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 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
2	C₂×C₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3121	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#482	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#451	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#448	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
22	C₇×#542	—	2	4	no	—
23	C₇×#542	C₂²	1	8	yes	—
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#126	—	2	1	no	—
26	C₂×C₇×#124	—	2	1	no	—
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₇×#123	—	2	1	no	—
29	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×#121	C₂²	1	1	yes	characteristic
32	C₇×#519	—	2	4	no	—
33	C₇×#519	C₂²	1	8	yes	complemented
34	C₂×C₄×C₇×Q₈	—	2	1	no	—
35	C₂×C₄×C₇×Q₈	—	2	1	no	—
36	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₇×#117	—	2	1	no	—
43	C₂×C₇×#117	—	2	1	no	—
44	C₂×C₇×#117	C₂²	1	1	yes	characteristic
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic
46	C₇×#485	C₂²	1	8	yes	complemented
47	C₇×#482	C₂²	1	8	yes	—
48	C₇×#477	C₂²	1	8	yes	complemented
49	C₇×#475	C₂²	1	8	yes	complemented
50	C₇×#464	C₂²	1	8	yes	complemented
51	C₇×#464	C₂²	1	8	yes	complemented
52	C₇×#451	C₂²	1	8	yes	complemented
53	C₇×#448	C₂²	1	8	yes	—
54	C₇×#441	C₂²	1	8	yes	complemented
55	C₇×#440	C₂²	1	8	yes	complemented
56	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
57	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
58	C₇×#433	C₂²	1	8	yes	complemented
59	C₂×C₇×#107	C₂²	1	1	yes	characteristic
60	C₂×C₇×#107	C₂²	1	1	yes	characteristic
61	C₂×C₇×#106	C₂²	1	1	yes	characteristic
62	C₂×C₇×#106	C₂²	1	1	yes	characteristic
63	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₇×#103	C₂²	1	1	yes	characteristic
66	C₂×C₇×#103	C₂²	1	1	yes	characteristic
67	C₂×C₇×#103	C₂²	1	1	yes	characteristic
68	C₂×C₇×#103	C₂²	1	1	yes	characteristic
69	C₂×C₇×#103	C₂²	1	1	yes	characteristic
70	C₂×C₇×#103	C₂²	1	1	yes	characteristic
71	C₂×C₇×#102	C₂²	1	1	yes	characteristic
72	C₂×C₇×#102	C₂²	1	1	yes	characteristic
73	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₇×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
77	C₂×#3121	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂²×C₇×Q₈	—	2	4	no	—
79	C₂²×C₇×Q₈	—	2	4	no	—
80	C₂²×C₇×Q₈	—	2	1	no	—
81	C₂²×C₇×Q₈	—	2	2	no	—
82	C₂²×C₇×Q₈	—	2	1	no	—
83	C₂²×C₇×Q₈	C₂³	1	4	yes	—
84	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×D₄	—	2	1	no	—
88	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
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×Q₁₆	—	2	4	no	—
93	C₂×C₇×Q₁₆	—	2	4	no	—
94	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
95	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
96	C₂×C₇×SD₁₆	—	2	4	no	—
97	C₂×C₇×SD₁₆	—	2	4	no	—
98	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
100	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
104	C₇×C₄⋊Q₈	—	2	2	no	—
105	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₇×#126	—	2	8	no	—
107	C₇×#124	—	2	8	no	—
108	C₇×#124	—	2	2	no	—
109	C₇×#124	C₂³	1	4	yes	—
110	C₇×#123	—	2	8	no	—
111	C₇×C₂²⋊Q₈	—	2	2	no	—
112	C₇×C₂²⋊Q₈	—	2	8	no	—
113	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₇×#121	—	2	2	no	—
115	C₇×#121	C₂³	1	4	yes	—
116	C₄×C₇×Q₈	—	2	8	no	—
117	C₄×C₇×Q₈	—	2	8	no	—
118	C₄×C₇×Q₈	—	2	2	no	—
119	C₄×C₇×Q₈	—	2	2	no	—
120	C₄×C₇×Q₈	—	2	2	no	—
121	C₄×C₇×Q₈	—	2	2	no	—
122	C₄×C₇×Q₈	—	2	2	no	—
123	C₄×C₇×Q₈	C₂³	1	4	yes	—
124	C₄×C₇×Q₈	C₂³	1	4	yes	—
125	C₄×C₇×Q₈	C₂³	1	4	yes	—
126	C₄×C₇×Q₈	C₂³	1	4	yes	—
127	C₄×C₇×Q₈	C₂³	1	4	yes	—
128	C₄×C₇×D₄	—	2	2	no	—
129	C₄×C₇×D₄	C₂³	1	4	yes	—
130	C₇×#117	—	2	2	no	—
131	C₇×#117	—	2	8	no	—
132	C₇×#117	—	2	8	no	—
133	C₇×#117	D₄	1	4	yes	—
134	C₇×#117	C₂³	1	4	yes	—
135	C₇×#117	C₂³	1	4	yes	—
136	C₂×C₇×C₄⋊C₄	—	2	1	no	—
137	C₂×C₇×C₄⋊C₄	—	2	1	no	—
138	C₂×C₇×C₄⋊C₄	—	2	1	no	—
139	C₂×C₇×C₄⋊C₄	—	2	1	no	—
140	C₂×C₇×C₄⋊C₄	—	2	1	no	—
141	C₂×C₇×C₄⋊C₄	—	2	1	no	—
142	C₂×C₇×C₄⋊C₄	—	2	1	no	—
143	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
144	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
145	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
151	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
156	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
157	C₂×C₄²×C₇	—	2	1	no	—
158	C₂×C₄²×C₇	—	2	1	no	—
159	C₂×C₄²×C₇	—	2	1	no	—
160	C₂×C₄²×C₇	—	2	1	no	—
161	C₂×C₄²×C₇	—	2	1	no	—
162	C₂×C₄²×C₇	—	2	1	no	—
163	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
165	C₇×#107	C₂³	1	4	yes	—
166	C₇×#107	C₂³	1	4	yes	—
167	C₇×#106	C₂³	1	4	yes	—
168	C₇×#106	C₂³	1	4	yes	—
169	C₇×C₄⋊C₈	C₂³	1	4	yes	—
170	C₇×C₄⋊C₈	C₂³	1	4	yes	—
171	C₇×#103	C₂³	1	4	yes	—
172	C₇×#103	C₂³	1	4	yes	—
173	C₇×#103	C₂³	1	4	yes	—
174	C₇×#103	C₂³	1	4	yes	—
175	C₇×#103	C₂³	1	4	yes	—
176	C₇×#103	C₂³	1	4	yes	—
177	C₇×#102	C₂³	1	4	yes	—
178	C₇×#102	C₂³	1	4	yes	—
179	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₇×#97	C₂³	1	4	yes	—
182	C₄×C₇×C₈	C₂³	1	4	yes	—
183	C₂×#542	C₂×C₇	1	1	yes	characteristic
184	C₂×#519	C₂×C₇	1	1	yes	characteristic, complemented
185	#3121	C₂×C₇	1	16	yes	direct product factor
186	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#482	C₂×C₇	1	1	yes	characteristic
188	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
189	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#451	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#448	C₂×C₇	1	1	yes	characteristic
194	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂⁴×C₇	—	2	1	no	—
200	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
201	C₂×C₇×Q₈	—	2	16	no	—
202	C₂×C₇×Q₈	—	2	8	no	—
203	C₂×C₇×Q₈	—	2	8	no	—
204	C₂×C₇×Q₈	—	2	8	no	—
205	C₂×C₇×Q₈	—	2	4	no	—
206	C₂×C₇×Q₈	—	2	1	no	—
207	C₂×C₇×Q₈	—	2	1	no	—
208	C₂×C₇×Q₈	—	2	1	no	—
209	C₂×C₇×Q₈	—	2	4	no	—
210	C₂×C₇×Q₈	—	2	2	no	—
211	C₂×C₇×Q₈	—	2	2	no	—
212	C₂×C₇×Q₈	—	2	2	no	—
213	C₂×C₇×Q₈	—	2	2	no	—
214	C₂×C₇×Q₈	—	8	2	no	—
215	C₂×C₇×Q₈	#41	1	4	yes	—
216	C₂×C₇×Q₈	#41	1	4	yes	—
217	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
218	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
219	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
220	C₂×C₇×D₄	—	2	4	no	—
221	C₂×C₇×D₄	—	2	1	no	—
222	C₂×C₇×D₄	—	2	2	no	—
223	C₂×C₇×D₄	—	2	2	no	—
224	C₂×C₇×D₄	—	8	2	no	—
225	C₂×C₇×D₄	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₇	—	2	8	no	—
227	C₂²×C₄×C₇	—	2	4	no	—
228	C₂²×C₄×C₇	—	2	1	no	—
229	C₂²×C₄×C₇	—	2	1	no	—
230	C₂²×C₄×C₇	—	2	2	no	—
231	C₂²×C₄×C₇	—	2	2	no	—
232	C₂²×C₄×C₇	—	2	1	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	4	no	—
238	C₂²×C₄×C₇	—	8	2	no	—
239	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
247	C₇×Q₁₆	—	2	8	no	—
248	C₇×Q₁₆	—	2	8	no	—
249	C₇×SD₁₆	—	2	8	no	—
250	C₇×SD₁₆	—	2	8	no	—
251	C₂×C₇×C₈	—	2	2	no	—
252	C₂×C₇×C₈	—	2	2	no	—
253	C₂×C₇×C₈	—	2	2	no	—
254	C₂×C₇×C₈	—	2	2	no	—
255	C₂×C₇×C₈	C₂⁴	1	2	yes	—
256	C₂×C₇×C₈	C₂⁴	1	2	yes	—
257	C₂×C₇×C₈	C₂⁴	1	2	yes	—
258	C₂×C₇×C₈	C₂⁴	1	2	yes	—
259	C₇×C₄⋊C₄	—	2	4	no	—
260	C₇×C₄⋊C₄	—	2	4	no	—
261	C₇×C₄⋊C₄	—	2	4	no	—
262	C₇×C₄⋊C₄	—	2	4	no	—
263	C₇×C₄⋊C₄	—	2	4	no	—
264	C₇×C₄⋊C₄	—	2	4	no	—
265	C₇×C₄⋊C₄	—	2	4	no	—
266	C₇×C₄⋊C₄	—	2	1	no	—
267	C₇×C₄⋊C₄	—	2	1	no	—
268	C₇×C₄⋊C₄	—	2	1	no	—
269	C₇×C₄⋊C₄	—	2	1	no	—
270	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
271	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
272	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
273	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
274	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
275	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
276	C₇×C₂²⋊C₄	—	2	4	no	—
277	C₇×C₂²⋊C₄	—	2	4	no	—
278	C₇×C₂²⋊C₄	—	2	4	no	—
279	C₇×C₂²⋊C₄	—	2	4	no	—
280	C₇×C₂²⋊C₄	—	2	4	no	—
281	C₇×C₂²⋊C₄	—	2	4	no	—
282	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
283	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
284	C₄²×C₇	—	2	4	no	—
285	C₄²×C₇	—	2	4	no	—
286	C₄²×C₇	—	2	4	no	—
287	C₄²×C₇	—	2	4	no	—
288	C₄²×C₇	—	2	4	no	—
289	C₄²×C₇	—	2	4	no	—
290	C₄²×C₇	C₂×D₄	1	2	yes	—
291	C₄²×C₇	C₂×D₄	1	2	yes	—
292	C₄²×C₇	C₂⁴	1	2	yes	—
293	C₄²×C₇	C₂⁴	1	2	yes	—
294	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
295	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
296	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
297	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
298	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
299	#542	—	2	4	no	—
300	#542	C₂²×C₇	1	8	yes	—
301	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
302	C₂×#126	—	2	1	no	—
303	C₂×#124	—	2	1	no	—
304	C₂×#124	C₂²×C₇	1	1	yes	characteristic
305	C₂×#123	—	2	1	no	—
306	C₂×C₂²⋊Q₈	—	2	1	no	—
307	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
308	C₂×#121	C₂²×C₇	1	1	yes	characteristic
309	#519	—	2	4	no	—
310	#519	C₂²×C₇	1	8	yes	complemented
311	C₂×C₄×Q₈	—	2	1	no	—
312	C₂×C₄×Q₈	—	2	1	no	—
313	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
314	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
315	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
316	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
318	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
319	C₂×#117	—	2	1	no	—
320	C₂×#117	—	2	1	no	—
321	C₂×#117	C₂²×C₇	1	1	yes	characteristic
322	C₂×#117	C₂²×C₇	1	1	yes	characteristic
323	#485	C₂²×C₇	1	8	yes	complemented
324	#482	C₂²×C₇	1	8	yes	—
325	#477	C₂²×C₇	1	8	yes	complemented
326	#475	C₂²×C₇	1	8	yes	complemented
327	#464	C₂²×C₇	1	8	yes	complemented
328	#464	C₂²×C₇	1	8	yes	complemented
329	#451	C₂²×C₇	1	8	yes	complemented
330	#448	C₂²×C₇	1	8	yes	—
331	#441	C₂²×C₇	1	8	yes	complemented
332	#440	C₂²×C₇	1	8	yes	complemented
333	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
334	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
335	#433	C₂²×C₇	1	8	yes	complemented
336	C₂×#107	C₂²×C₇	1	1	yes	characteristic
337	C₂×#107	C₂²×C₇	1	1	yes	characteristic
338	C₂×#106	C₂²×C₇	1	1	yes	characteristic
339	C₂×#106	C₂²×C₇	1	1	yes	characteristic
340	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
341	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
342	C₂×#103	C₂²×C₇	1	1	yes	characteristic
343	C₂×#103	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×#103	C₂²×C₇	1	1	yes	characteristic
347	C₂×#103	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×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
351	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
352	C₂×#97	C₂²×C₇	1	1	yes	characteristic
353	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
354	C₂³×C₇	—	2	2	no	—
355	C₂³×C₇	—	2	2	no	—
356	C₂³×C₇	—	2	2	no	—
357	C₂³×C₇	—	2	2	no	—
358	C₂³×C₇	—	4	2	no	—
359	C₂³×C₇	—	4	2	no	—
360	C₂³×C₇	—	4	2	no	—
361	C₂³×C₇	C₂²×D₄	1	2	yes	—
362	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
363	C₇×Q₈	—	2	16	no	—
364	C₇×Q₈	—	2	4	no	—
365	C₇×Q₈	—	2	4	no	—
366	C₇×Q₈	—	2	2	no	—
367	C₇×Q₈	—	2	2	no	—
368	C₇×Q₈	—	2	2	no	—
369	C₇×Q₈	—	2	2	no	—
370	C₇×Q₈	—	4	2	no	—
371	C₇×Q₈	—	8	4	no	—
372	C₇×Q₈	C₂×#41	1	4	yes	—
373	C₇×Q₈	C₂×#41	1	4	yes	—
374	C₇×D₄	—	2	2	no	—
375	C₇×D₄	—	2	2	no	—
376	C₇×D₄	—	4	2	no	—
377	C₇×D₄	—	8	4	no	—
378	C₂×C₄×C₇	—	2	16	no	—
379	C₂×C₄×C₇	—	2	4	no	—
380	C₂×C₄×C₇	—	2	4	no	—
381	C₂×C₄×C₇	—	2	2	no	—
382	C₂×C₄×C₇	—	2	2	no	—
383	C₂×C₄×C₇	—	2	2	no	—
384	C₂×C₄×C₇	—	2	2	no	—
385	C₂×C₄×C₇	—	2	2	no	—
386	C₂×C₄×C₇	—	2	2	no	—
387	C₂×C₄×C₇	—	2	2	no	—
388	C₂×C₄×C₇	—	2	4	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	2	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	—	4	2	no	—
397	C₂×C₄×C₇	—	4	2	no	—
398	C₂×C₄×C₇	—	4	2	no	—
399	C₂×C₄×C₇	—	4	2	no	—
400	C₂×C₄×C₇	—	4	2	no	—
401	C₂×C₄×C₇	—	8	4	no	—
402	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₇	C₂×#41	1	2	yes	—
409	C₂×C₄×C₇	C₂×#41	1	2	yes	—
410	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
411	C₇×C₈	—	2	2	no	—
412	C₇×C₈	—	2	2	no	—
413	C₇×C₈	—	2	2	no	—
414	C₇×C₈	—	2	2	no	—
415	C₂²×Q₈	—	2	4	no	—
416	C₂²×Q₈	—	2	4	no	—
417	C₂²×Q₈	—	2	1	no	—
418	C₂²×Q₈	—	2	2	no	—
419	C₂²×Q₈	—	2	1	no	—
420	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
421	C₂²×Q₈	C₂³×C₇	1	4	yes	—
422	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
423	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
429	C₂×Q₁₆	—	2	4	no	—
430	C₂×Q₁₆	—	2	4	no	—
431	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
432	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
433	C₂×SD₁₆	—	2	4	no	—
434	C₂×SD₁₆	—	2	4	no	—
435	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
436	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
437	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
441	C₄⋊Q₈	—	2	2	no	—
442	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
443	#126	—	2	8	no	—
444	#124	—	2	8	no	—
445	#124	—	2	2	no	—
446	#124	C₂³×C₇	1	4	yes	—
447	#123	—	2	8	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	8	no	—
450	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
451	#121	—	2	2	no	—
452	#121	C₂³×C₇	1	4	yes	—
453	C₄×Q₈	—	2	8	no	—
454	C₄×Q₈	—	2	8	no	—
455	C₄×Q₈	—	2	2	no	—
456	C₄×Q₈	—	2	2	no	—
457	C₄×Q₈	—	2	2	no	—
458	C₄×Q₈	—	2	2	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	C₂³×C₇	1	4	yes	—
461	C₄×Q₈	C₂³×C₇	1	4	yes	—
462	C₄×Q₈	C₂³×C₇	1	4	yes	—
463	C₄×Q₈	C₂³×C₇	1	4	yes	—
464	C₄×Q₈	C₂³×C₇	1	4	yes	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	C₂³×C₇	1	4	yes	—
467	#117	—	2	2	no	—
468	#117	—	2	8	no	—
469	#117	—	2	8	no	—
470	#117	C₇×D₄	1	4	yes	—
471	#117	C₂³×C₇	1	4	yes	—
472	#117	C₂³×C₇	1	4	yes	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
494	C₂×C₄²	—	2	1	no	—
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	—	2	1	no	—
497	C₂×C₄²	—	2	1	no	—
498	C₂×C₄²	—	2	1	no	—
499	C₂×C₄²	—	2	1	no	—
500	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
502	#107	C₂³×C₇	1	4	yes	—
503	#107	C₂³×C₇	1	4	yes	—
504	#106	C₂³×C₇	1	4	yes	—
505	#106	C₂³×C₇	1	4	yes	—
506	C₄⋊C₈	C₂³×C₇	1	4	yes	—
507	C₄⋊C₈	C₂³×C₇	1	4	yes	—
508	#103	C₂³×C₇	1	4	yes	—
509	#103	C₂³×C₇	1	4	yes	—
510	#103	C₂³×C₇	1	4	yes	—
511	#103	C₂³×C₇	1	4	yes	—
512	#103	C₂³×C₇	1	4	yes	—
513	#103	C₂³×C₇	1	4	yes	—
514	#102	C₂³×C₇	1	4	yes	—
515	#102	C₂³×C₇	1	4	yes	—
516	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
517	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
518	#97	C₂³×C₇	1	4	yes	—
519	C₄×C₈	C₂³×C₇	1	4	yes	—
520	C₂²×C₇	—	2	2	no	—
521	C₂²×C₇	—	2	2	no	—
522	C₂²×C₇	—	2	2	no	—
523	C₂²×C₇	—	4	4	no	—
524	C₂²×C₇	—	4	2	no	—
525	C₂²×C₇	—	4	2	no	—
526	C₂²×C₇	—	4	2	no	—
527	C₂²×C₇	—	8	4	no	—
528	C₂²×C₇	#525	1	2	yes	—
529	C₂²×C₇	#577	1	2	yes	—
530	C₂²×C₇	#578	1	2	yes	—
531	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₇	—	2	4	no	—
533	C₄×C₇	—	2	4	no	—
534	C₄×C₇	—	2	2	no	—
535	C₄×C₇	—	2	2	no	—
536	C₄×C₇	—	2	2	no	—
537	C₄×C₇	—	2	2	no	—
538	C₄×C₇	—	2	2	no	—
539	C₄×C₇	—	4	2	no	—
540	C₄×C₇	—	4	2	no	—
541	C₄×C₇	—	4	2	no	—
542	C₄×C₇	—	4	2	no	—
543	C₄×C₇	—	4	2	no	—
544	C₄×C₇	#525	1	2	yes	—
545	C₄×C₇	C₂²×#41	1	1	yes	characteristic
546	C₄×C₇	C₂²×#41	1	1	yes	characteristic
547	C₂⁴	—	2	1	no	—
548	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
549	C₂×Q₈	—	2	16	no	—
550	C₂×Q₈	—	2	8	no	—
551	C₂×Q₈	—	2	8	no	—
552	C₂×Q₈	—	2	8	no	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	8	2	no	—
563	C₂×Q₈	C₇×#41	1	4	yes	—
564	C₂×Q₈	C₇×#41	1	4	yes	—
565	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
566	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
567	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	8	2	no	—
573	C₂×D₄	C₂⁴×C₇	1	2	yes	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	8	2	no	—
587	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
588	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
589	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
590	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
591	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
592	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
595	Q₁₆	—	2	8	no	—
596	Q₁₆	—	2	8	no	—
597	SD₁₆	—	2	8	no	—
598	SD₁₆	—	2	8	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	2	2	no	—
602	C₂×C₈	—	2	2	no	—
603	C₂×C₈	C₂⁴×C₇	1	2	yes	—
604	C₂×C₈	C₂⁴×C₇	1	2	yes	—
605	C₂×C₈	C₂⁴×C₇	1	2	yes	—
606	C₂×C₈	C₂⁴×C₇	1	2	yes	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
619	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
620	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
631	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	C₂×C₇×D₄	1	2	yes	—
639	C₄²	C₂×C₇×D₄	1	2	yes	—
640	C₄²	C₂⁴×C₇	1	2	yes	—
641	C₄²	C₂⁴×C₇	1	2	yes	—
642	C₂×C₇	—	4	2	no	—
643	C₂×C₇	—	8	2	no	—
644	C₂×C₇	#3121	1	4	yes	direct product factor
645	C₂×C₇	C₂×#525	1	1	yes	characteristic
646	C₂×C₇	C₂×#577	1	1	yes	characteristic
647	C₂×C₇	C₂×#578	1	1	yes	characteristic
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	C₂²×C₇×D₄	1	2	yes	—
656	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
657	Q₈	—	2	16	no	—
658	Q₈	—	2	2	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	2	4	no	—
661	Q₈	—	2	4	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	4	2	no	—
665	Q₈	—	8	4	no	—
666	Q₈	C₂×C₇×#41	1	4	yes	—
667	Q₈	C₂×C₇×#41	1	4	yes	—
668	D₄	—	2	2	no	—
669	D₄	—	2	2	no	—
670	D₄	—	4	2	no	—
671	D₄	—	8	4	no	—
672	C₂×C₄	—	2	16	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
697	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
698	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
699	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
700	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
701	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
702	C₂×C₄	C₂×C₇×#41	1	2	yes	—
703	C₂×C₄	C₂×C₇×#41	1	2	yes	—
704	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
705	C₈	—	2	2	no	—
706	C₈	—	2	2	no	—
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₇	C₂×#3121	1	1	yes	characteristic, direct product factor, Sylow
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	8	4	no	—
718	C₂²	C₇×#525	1	2	yes	—
719	C₂²	C₇×#577	1	2	yes	—
720	C₂²	C₇×#578	1	2	yes	—
721	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	4	no	—
728	C₄	—	2	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	C₇×#525	1	2	yes	—
735	C₄	C₂²×C₇×#41	1	1	yes	characteristic
736	C₄	C₂²×C₇×#41	1	1	yes	characteristic
737	C₂	—	4	2	no	—
738	C₂	—	8	2	no	—
739	C₂	C₇×#3121	1	4	yes	direct product factor
740	C₂	C₂×C₇×#525	1	1	yes	characteristic
741	C₂	C₂×C₇×#577	1	1	yes	characteristic
742	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#121	C₂²
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
2. C₂×C₇×#519	C₂	semidirect
3. C₇×#3121	C₂	direct (N × H)
4. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#477	C₂	semidirect
7. C₂×C₇×#475	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
9. C₂×C₇×#464	C₂	semidirect
10. C₂×C₇×#451	C₂	semidirect
12. C₂×C₇×#441	C₂	semidirect
13. C₂×C₇×#440	C₂	semidirect
14. C₂×C₄×C₇×Q₁₆	C₂	semidirect
15. C₂×C₄×C₇×SD₁₆	C₂	semidirect
16. C₂×C₇×#433	C₂	semidirect
33. C₇×#519	C₂²	semidirect
46. C₇×#485	C₂²	semidirect
48. C₇×#477	C₂²	semidirect
49. C₇×#475	C₂²	semidirect
50. C₇×#464	C₂²	semidirect
51. C₇×#464	C₂²	semidirect
52. C₇×#451	C₂²	semidirect
54. C₇×#441	C₂²	semidirect
55. C₇×#440	C₂²	semidirect
56. C₄×C₇×Q₁₆	C₂²	semidirect
57. C₄×C₇×SD₁₆	C₂²	semidirect
58. C₇×#433	C₂²	semidirect
77. C₂×#3121	C₇	direct (N × H)
184. C₂×#519	C₂×C₇	semidirect
185. #3121	C₂×C₇	direct (N × H)
186. C₂×#485	C₂×C₇	semidirect
188. C₂×#477	C₂×C₇	semidirect
189. C₂×#475	C₂×C₇	semidirect
190. C₂×#464	C₂×C₇	semidirect
191. C₂×#464	C₂×C₇	semidirect
192. C₂×#451	C₂×C₇	semidirect
194. C₂×#441	C₂×C₇	semidirect
195. C₂×#440	C₂×C₇	semidirect
196. C₂×C₄×Q₁₆	C₂×C₇	semidirect
197. C₂×C₄×SD₁₆	C₂×C₇	semidirect
198. C₂×#433	C₂×C₇	semidirect
310. #519	C₂²×C₇	semidirect
323. #485	C₂²×C₇	semidirect
325. #477	C₂²×C₇	semidirect
326. #475	C₂²×C₇	semidirect
327. #464	C₂²×C₇	semidirect
328. #464	C₂²×C₇	semidirect
329. #451	C₂²×C₇	semidirect
331. #441	C₂²×C₇	semidirect
332. #440	C₂²×C₇	semidirect
333. C₄×Q₁₆	C₂²×C₇	semidirect
334. C₄×SD₁₆	C₂²×C₇	semidirect
335. #433	C₂²×C₇	semidirect
644. C₂×C₇	#3121	direct (N × H)
709. C₇	C₂×#3121	direct (N × H)
739. C₂	C₇×#3121	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×#519	2
C₇×#3121	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#477	2
C₂×C₇×#475	2
C₂×C₇×#464	2
C₂×C₇×#451	2
C₂×C₇×#448	2
C₂×C₇×#441	2
C₂×C₇×#440	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₇×#433	2
C₂×#3121	7

Subgroups — C2×C7×#3121 #13237766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3121 #13237766