Subgroups — C₂×C₇×#3312 #13238347

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#552	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×D₄×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#3312	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic
15	C₂×C₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#552	—	2	4	no	—
25	C₇×#552	C₂²	1	8	yes	—
26	C₇×D₄×Q₈	—	2	4	no	—
27	C₇×D₄×Q₈	C₂²	1	8	yes	—
28	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
29	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×#126	—	2	1	no	—
31	C₂×C₇×#125	—	2	1	no	—
32	C₂×C₇×#125	C₂²	1	1	yes	characteristic
33	C₂×C₇×#123	—	2	1	no	—
34	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	—	2	1	no	—
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₇×#117	—	2	1	no	—
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₇×#491	C₂²	1	8	yes	complemented
48	C₇×#485	C₂²	1	8	yes	complemented
49	C₇×#483	C₂²	1	8	yes	complemented
50	C₇×#479	C₂²	1	8	yes	complemented
51	C₇×#470	C₂²	1	8	yes	complemented
52	C₇×#467	C₂²	1	8	yes	complemented
53	C₇×#462	C₂²	1	8	yes	complemented
54	C₇×#451	C₂²	1	8	yes	complemented
55	C₇×#451	C₂²	1	8	yes	complemented
56	C₇×#441	C₂²	1	8	yes	complemented
57	C₇×#435	C₂²	1	8	yes	—
58	C₂×C₇×#107	C₂²	1	1	yes	characteristic
59	C₂×C₇×#106	C₂²	1	1	yes	characteristic
60	C₂×C₇×#106	C₂²	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₇×#419	C₂²	1	8	yes	complemented
63	C₂×C₇×#103	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×#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×#103	C₂²	1	1	yes	characteristic
72	C₂×C₇×#103	C₂²	1	1	yes	characteristic
73	C₂×C₇×#103	C₂²	1	8	yes	complemented
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₇×#97	C₂²	1	1	yes	characteristic
77	C₂×#3312	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂²×C₇×Q₈	—	2	1	no	—
79	C₂²×C₇×Q₈	—	2	1	no	—
80	C₂²×C₇×Q₈	—	2	2	no	—
81	C₂²×C₇×Q₈	—	2	2	no	—
82	C₂²×C₇×Q₈	—	2	4	no	—
83	C₂²×C₇×Q₈	—	2	4	no	—
84	C₂²×C₇×Q₈	—	4	2	no	—
85	C₂²×C₇×Q₈	—	4	2	no	—
86	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×Q₈	C₂³	1	4	yes	—
90	C₂²×C₇×Q₈	C₂³	1	4	yes	—
91	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
92	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₇	—	2	1	no	—
94	C₂³×C₄×C₇	—	2	1	no	—
95	C₂³×C₄×C₇	—	2	1	no	—
96	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₂×C₇×Q₁₆	—	2	4	no	—
99	C₂×C₇×Q₁₆	—	4	2	no	—
100	C₂×C₇×Q₁₆	—	4	2	no	—
101	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
102	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₇×M₁₆	—	4	2	no	—
105	C₂×C₇×M₁₆	C₂³	1	4	yes	—
106	C₂²×C₇×C₈	—	4	2	no	—
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	4	yes	—
112	C₇×C₄⋊Q₈	—	2	8	no	—
113	C₇×C₄⋊Q₈	—	2	2	no	—
114	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₇×#126	—	2	8	no	—
116	C₇×#125	—	2	8	no	—
117	C₇×#125	—	2	2	no	—
118	C₇×#125	C₂³	1	4	yes	—
119	C₇×#123	—	2	8	no	—
120	C₇×C₂²⋊Q₈	—	2	2	no	—
121	C₇×C₂²⋊Q₈	—	2	2	no	—
122	C₇×C₂²⋊Q₈	—	2	2	no	—
123	C₇×C₂²⋊Q₈	—	2	2	no	—
124	C₇×C₂²⋊Q₈	—	2	8	no	—
125	C₇×C₂²⋊Q₈	—	2	8	no	—
126	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₄×C₇×Q₈	—	2	2	no	—
131	C₄×C₇×Q₈	—	2	2	no	—
132	C₄×C₇×Q₈	C₂³	1	4	yes	—
133	C₄×C₇×Q₈	C₂³	1	4	yes	—
134	C₄×C₇×D₄	—	2	8	no	—
135	C₄×C₇×D₄	D₄	1	4	yes	—
136	C₄×C₇×D₄	C₂³	1	4	yes	—
137	C₇×#117	—	2	2	no	—
138	C₇×#117	—	2	8	no	—
139	C₇×#117	C₂³	1	4	yes	—
140	C₂×C₇×C₄⋊C₄	—	2	1	no	—
141	C₂×C₇×C₄⋊C₄	—	2	2	no	—
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	—	2	1	no	—
148	C₂×C₇×C₄⋊C₄	—	2	1	no	—
149	C₂×C₇×C₄⋊C₄	—	2	1	no	—
150	C₂×C₇×C₄⋊C₄	—	2	1	no	—
151	C₂×C₇×C₄⋊C₄	—	2	1	no	—
152	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
163	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
164	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₇	—	2	1	no	—
166	C₂×C₄²×C₇	—	2	1	no	—
167	C₂×C₄²×C₇	—	2	1	no	—
168	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
169	C₇×#107	C₂³	1	4	yes	—
170	C₇×#106	C₂³	1	4	yes	—
171	C₇×#106	C₂³	1	4	yes	—
172	C₇×C₄⋊C₈	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×#103	C₂³	1	4	yes	—
178	C₇×#103	C₂³	1	4	yes	—
179	C₇×#103	C₂³	1	4	yes	—
180	C₇×#103	C₂³	1	4	yes	—
181	C₇×#103	C₂³	1	4	yes	—
182	C₇×#103	C₂³	1	4	yes	—
183	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₇×#97	C₂³	1	4	yes	—
186	C₂×#552	C₂×C₇	1	1	yes	characteristic
187	C₂×D₄×Q₈	C₂×C₇	1	1	yes	characteristic
188	#3312	C₂×C₇	1	16	yes	direct product factor
189	C₂×#491	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#483	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#470	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#467	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#451	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#451	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂×#435	C₂×C₇	1	1	yes	characteristic
200	C₂×#419	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂²×#103	C₂×C₇	1	1	yes	characteristic, complemented
202	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
203	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
204	C₂×C₇×Q₈	—	2	1	no	—
205	C₂×C₇×Q₈	—	2	1	no	—
206	C₂×C₇×Q₈	—	2	4	no	—
207	C₂×C₇×Q₈	—	2	4	no	—
208	C₂×C₇×Q₈	—	2	1	no	—
209	C₂×C₇×Q₈	—	2	1	no	—
210	C₂×C₇×Q₈	—	2	2	no	—
211	C₂×C₇×Q₈	—	2	8	no	—
212	C₂×C₇×Q₈	—	2	8	no	—
213	C₂×C₇×Q₈	—	2	2	no	—
214	C₂×C₇×Q₈	—	2	2	no	—
215	C₂×C₇×Q₈	—	2	2	no	—
216	C₂×C₇×Q₈	—	2	2	no	—
217	C₂×C₇×Q₈	—	2	2	no	—
218	C₂×C₇×Q₈	—	2	2	no	—
219	C₂×C₇×Q₈	—	4	4	no	—
220	C₂×C₇×Q₈	—	4	4	no	—
221	C₂×C₇×Q₈	—	4	4	no	—
222	C₂×C₇×Q₈	—	4	4	no	—
223	C₂×C₇×Q₈	—	4	8	no	—
224	C₂×C₇×Q₈	—	4	8	no	—
225	C₂×C₇×Q₈	#41	1	4	yes	—
226	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
227	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
228	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
229	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₇	—	2	1	no	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	2	no	—
235	C₂²×C₄×C₇	—	2	2	no	—
236	C₂²×C₄×C₇	—	2	2	no	—
237	C₂²×C₄×C₇	—	2	4	no	—
238	C₂²×C₄×C₇	—	2	4	no	—
239	C₂²×C₄×C₇	—	2	4	no	—
240	C₂²×C₄×C₇	—	2	1	no	—
241	C₂²×C₄×C₇	—	2	1	no	—
242	C₂²×C₄×C₇	—	2	1	no	—
243	C₂²×C₄×C₇	—	2	1	no	—
244	C₂²×C₄×C₇	—	2	1	no	—
245	C₂²×C₄×C₇	—	2	1	no	—
246	C₂²×C₄×C₇	—	2	1	no	—
247	C₂²×C₄×C₇	—	4	4	no	—
248	C₂²×C₄×C₇	—	4	4	no	—
249	C₂²×C₄×C₇	—	4	4	no	—
250	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
259	C₇×Q₁₆	—	2	8	no	—
260	C₇×Q₁₆	—	4	4	no	—
261	C₇×Q₁₆	—	4	4	no	—
262	C₇×M₁₆	—	4	4	no	—
263	C₂×C₇×C₈	—	2	2	no	—
264	C₂×C₇×C₈	—	2	2	no	—
265	C₂×C₇×C₈	—	2	2	no	—
266	C₂×C₇×C₈	—	2	2	no	—
267	C₂×C₇×C₈	—	4	4	no	—
268	C₂×C₇×C₈	C₂⁴	1	2	yes	—
269	C₂×C₇×C₈	C₂⁴	1	2	yes	—
270	C₂×C₇×C₈	C₂⁴	1	2	yes	—
271	C₂×C₇×C₈	C₂⁴	1	2	yes	—
272	C₇×C₄⋊C₄	—	2	1	no	—
273	C₇×C₄⋊C₄	—	2	1	no	—
274	C₇×C₄⋊C₄	—	2	4	no	—
275	C₇×C₄⋊C₄	—	2	4	no	—
276	C₇×C₄⋊C₄	—	2	4	no	—
277	C₇×C₄⋊C₄	—	2	4	no	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	4	no	—
281	C₇×C₄⋊C₄	—	2	4	no	—
282	C₇×C₄⋊C₄	—	2	4	no	—
283	C₇×C₄⋊C₄	—	2	4	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	1	no	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₇×C₂²⋊C₄	—	2	4	no	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
298	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
299	C₄²×C₇	—	2	4	no	—
300	C₄²×C₇	—	2	4	no	—
301	C₄²×C₇	—	2	4	no	—
302	C₄²×C₇	C₂×D₄	1	2	yes	—
303	C₄²×C₇	C₂⁴	1	2	yes	—
304	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
305	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
306	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
307	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
308	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
309	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
310	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
311	#552	—	2	4	no	—
312	#552	C₂²×C₇	1	8	yes	—
313	D₄×Q₈	—	2	4	no	—
314	D₄×Q₈	C₂²×C₇	1	8	yes	—
315	C₂×C₄⋊Q₈	—	2	1	no	—
316	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
317	C₂×#126	—	2	1	no	—
318	C₂×#125	—	2	1	no	—
319	C₂×#125	C₂²×C₇	1	1	yes	characteristic
320	C₂×#123	—	2	1	no	—
321	C₂×C₂²⋊Q₈	—	2	1	no	—
322	C₂×C₂²⋊Q₈	—	2	1	no	—
323	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
324	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
325	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
326	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
328	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
329	C₂×C₄×D₄	—	2	1	no	—
330	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
331	C₂×#117	—	2	1	no	—
332	C₂×#117	C₂²×C₇	1	1	yes	characteristic
333	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
334	#491	C₂²×C₇	1	8	yes	complemented
335	#485	C₂²×C₇	1	8	yes	complemented
336	#483	C₂²×C₇	1	8	yes	complemented
337	#479	C₂²×C₇	1	8	yes	complemented
338	#470	C₂²×C₇	1	8	yes	complemented
339	#467	C₂²×C₇	1	8	yes	complemented
340	#462	C₂²×C₇	1	8	yes	complemented
341	#451	C₂²×C₇	1	8	yes	complemented
342	#451	C₂²×C₇	1	8	yes	complemented
343	#441	C₂²×C₇	1	8	yes	complemented
344	#435	C₂²×C₇	1	8	yes	—
345	C₂×#107	C₂²×C₇	1	1	yes	characteristic
346	C₂×#106	C₂²×C₇	1	1	yes	characteristic
347	C₂×#106	C₂²×C₇	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
349	#419	C₂²×C₇	1	8	yes	complemented
350	C₂×#103	C₂²×C₇	1	1	yes	characteristic
351	C₂×#103	C₂²×C₇	1	1	yes	characteristic
352	C₂×#103	C₂²×C₇	1	1	yes	characteristic
353	C₂×#103	C₂²×C₇	1	1	yes	characteristic
354	C₂×#103	C₂²×C₇	1	1	yes	characteristic
355	C₂×#103	C₂²×C₇	1	1	yes	characteristic
356	C₂×#103	C₂²×C₇	1	1	yes	characteristic
357	C₂×#103	C₂²×C₇	1	1	yes	characteristic
358	C₂×#103	C₂²×C₇	1	1	yes	characteristic
359	C₂×#103	C₂²×C₇	1	1	yes	characteristic
360	C₂×#103	C₂²×C₇	1	8	yes	complemented
361	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
363	C₂×#97	C₂²×C₇	1	1	yes	characteristic
364	C₂³×C₇	—	2	2	no	—
365	C₂³×C₇	—	2	2	no	—
366	C₂³×C₇	—	2	2	no	—
367	C₂³×C₇	—	2	2	no	—
368	C₂³×C₇	—	2	2	no	—
369	C₂³×C₇	#137	1	4	yes	—
370	C₂³×C₇	C₂²×D₄	1	2	yes	—
371	C₂³×C₇	C₂²×D₄	1	2	yes	—
372	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
373	C₇×Q₈	—	2	4	no	—
374	C₇×Q₈	—	2	2	no	—
375	C₇×Q₈	—	2	2	no	—
376	C₇×Q₈	—	2	2	no	—
377	C₇×Q₈	—	2	2	no	—
378	C₇×Q₈	—	2	2	no	—
379	C₇×Q₈	—	2	2	no	—
380	C₇×Q₈	—	2	2	no	—
381	C₇×Q₈	—	4	8	no	—
382	C₇×Q₈	—	4	8	no	—
383	C₇×Q₈	—	4	2	no	—
384	C₇×Q₈	—	4	2	no	—
385	C₇×Q₈	—	4	2	no	—
386	C₇×Q₈	C₂×#41	1	4	yes	—
387	C₇×D₄	—	2	8	no	—
388	C₂×C₄×C₇	—	2	2	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	4	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	4	no	—
395	C₂×C₄×C₇	—	2	4	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	2	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	—	2	2	no	—
406	C₂×C₄×C₇	—	2	2	no	—
407	C₂×C₄×C₇	—	4	8	no	—
408	C₂×C₄×C₇	—	4	8	no	—
409	C₂×C₄×C₇	—	4	2	no	—
410	C₂×C₄×C₇	—	4	2	no	—
411	C₂×C₄×C₇	—	4	2	no	—
412	C₂×C₄×C₇	—	4	8	no	—
413	C₂×C₄×C₇	—	4	2	no	—
414	C₂×C₄×C₇	—	4	2	no	—
415	C₂×C₄×C₇	—	4	2	no	—
416	C₂×C₄×C₇	—	4	2	no	—
417	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₇	C₂×#41	1	2	yes	—
423	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
424	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
425	C₇×C₈	—	2	2	no	—
426	C₇×C₈	—	2	2	no	—
427	C₇×C₈	—	2	2	no	—
428	C₇×C₈	—	2	2	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×Q₈	—	2	1	no	—
431	C₂²×Q₈	—	2	2	no	—
432	C₂²×Q₈	—	2	2	no	—
433	C₂²×Q₈	—	2	4	no	—
434	C₂²×Q₈	—	2	4	no	—
435	C₂²×Q₈	—	4	2	no	—
436	C₂²×Q₈	—	4	2	no	—
437	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
438	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
439	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₇	1	4	yes	—
441	C₂²×Q₈	C₂³×C₇	1	4	yes	—
442	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
443	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	—	2	1	no	—
447	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
449	C₂×Q₁₆	—	2	4	no	—
450	C₂×Q₁₆	—	4	2	no	—
451	C₂×Q₁₆	—	4	2	no	—
452	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
453	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
454	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
455	C₂×M₁₆	—	4	2	no	—
456	C₂×M₁₆	C₂³×C₇	1	4	yes	—
457	C₂²×C₈	—	4	2	no	—
458	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
460	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₇	1	4	yes	—
463	C₄⋊Q₈	—	2	8	no	—
464	C₄⋊Q₈	—	2	2	no	—
465	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
466	#126	—	2	8	no	—
467	#125	—	2	8	no	—
468	#125	—	2	2	no	—
469	#125	C₂³×C₇	1	4	yes	—
470	#123	—	2	8	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	8	no	—
476	C₂²⋊Q₈	—	2	8	no	—
477	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
478	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
479	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
480	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×Q₈	C₂³×C₇	1	4	yes	—
484	C₄×Q₈	C₂³×C₇	1	4	yes	—
485	C₄×D₄	—	2	8	no	—
486	C₄×D₄	C₇×D₄	1	4	yes	—
487	C₄×D₄	C₂³×C₇	1	4	yes	—
488	#117	—	2	2	no	—
489	#117	—	2	8	no	—
490	#117	C₂³×C₇	1	4	yes	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
520	#107	C₂³×C₇	1	4	yes	—
521	#106	C₂³×C₇	1	4	yes	—
522	#106	C₂³×C₇	1	4	yes	—
523	C₄⋊C₈	C₂³×C₇	1	4	yes	—
524	#103	C₂³×C₇	1	4	yes	—
525	#103	C₂³×C₇	1	4	yes	—
526	#103	C₂³×C₇	1	4	yes	—
527	#103	C₂³×C₇	1	4	yes	—
528	#103	C₂³×C₇	1	4	yes	—
529	#103	C₂³×C₇	1	4	yes	—
530	#103	C₂³×C₇	1	4	yes	—
531	#103	C₂³×C₇	1	4	yes	—
532	#103	C₂³×C₇	1	4	yes	—
533	#103	C₂³×C₇	1	4	yes	—
534	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
535	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
536	#97	C₂³×C₇	1	4	yes	—
537	C₂²×C₇	—	2	2	no	—
538	C₂²×C₇	—	2	8	no	—
539	C₂²×C₇	—	2	2	no	—
540	C₂²×C₇	—	2	2	no	—
541	C₂²×C₇	—	2	2	no	—
542	C₂²×C₇	—	2	2	no	—
543	C₂²×C₇	—	4	4	no	—
544	C₂²×C₇	#546	1	2	yes	—
545	C₂²×C₇	C₂×#137	1	4	yes	—
546	C₂²×C₇	C₂×#137	1	2	yes	—
547	C₂²×C₇	#578	1	2	yes	—
548	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₇	—	2	2	no	—
550	C₄×C₇	—	2	2	no	—
551	C₄×C₇	—	2	4	no	—
552	C₄×C₇	—	2	2	no	—
553	C₄×C₇	—	2	2	no	—
554	C₄×C₇	—	4	2	no	—
555	C₄×C₇	—	4	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	#546	1	2	yes	—
562	C₄×C₇	C₂²×#41	1	1	yes	characteristic
563	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
565	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	8	no	—
574	C₂×Q₈	—	2	8	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	4	4	no	—
582	C₂×Q₈	—	4	4	no	—
583	C₂×Q₈	—	4	4	no	—
584	C₂×Q₈	—	4	4	no	—
585	C₂×Q₈	—	4	8	no	—
586	C₂×Q₈	—	4	8	no	—
587	C₂×Q₈	C₇×#41	1	4	yes	—
588	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
589	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
590	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	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	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	—	4	4	no	—
611	C₂²×C₄	—	4	4	no	—
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	1	yes	characteristic
615	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
616	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
617	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
621	Q₁₆	—	2	8	no	—
622	Q₁₆	—	4	4	no	—
623	Q₁₆	—	4	4	no	—
624	M₁₆	—	4	4	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	4	4	no	—
630	C₂×C₈	C₂⁴×C₇	1	2	yes	—
631	C₂×C₈	C₂⁴×C₇	1	2	yes	—
632	C₂×C₈	C₂⁴×C₇	1	2	yes	—
633	C₂×C₈	C₂⁴×C₇	1	2	yes	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
650	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
651	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
660	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
661	C₄²	—	2	4	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	2	4	no	—
664	C₄²	C₂×C₇×D₄	1	2	yes	—
665	C₄²	C₂⁴×C₇	1	2	yes	—
666	C₂×C₇	—	2	4	no	—
667	C₂×C₇	—	4	2	no	—
668	C₂×C₇	#3312	1	4	yes	direct product factor
669	C₂×C₇	C₂×#546	1	1	yes	characteristic
670	C₂×C₇	C₂²×#137	1	1	yes	characteristic
671	C₂×C₇	C₂×#578	1	1	yes	characteristic
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	C₇×#137	1	4	yes	—
678	C₂³	C₂²×C₇×D₄	1	2	yes	—
679	C₂³	C₂²×C₇×D₄	1	2	yes	—
680	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
681	Q₈	—	2	2	no	—
682	Q₈	—	2	4	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	4	8	no	—
690	Q₈	—	4	8	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	4	2	no	—
694	Q₈	C₂×C₇×#41	1	4	yes	—
695	D₄	—	2	8	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	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	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	8	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
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	1	yes	characteristic
730	C₂×C₄	C₂×C₇×#41	1	2	yes	—
731	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
732	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
733	C₈	—	2	2	no	—
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	—	2	2	no	—
737	C₇	C₂×#3312	1	1	yes	characteristic, direct product factor, Sylow
738	C₂²	—	2	2	no	—
739	C₂²	—	2	8	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	4	4	no	—
745	C₂²	C₇×#546	1	2	yes	—
746	C₂²	C₂×C₇×#137	1	4	yes	—
747	C₂²	C₂×C₇×#137	1	2	yes	—
748	C₂²	C₇×#578	1	2	yes	—
749	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	4	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	C₇×#546	1	2	yes	—
763	C₄	C₂²×C₇×#41	1	1	yes	characteristic
764	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
765	C₂	—	2	4	no	—
766	C₂	—	4	2	no	—
767	C₂	C₇×#3312	1	4	yes	direct product factor
768	C₂	C₂×C₇×#546	1	1	yes	characteristic
769	C₂	C₂²×C₇×#137	1	1	yes	characteristic
770	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	C₂²×C₇×D₄	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#3312	C₂	direct (N × H)
4. C₂×C₇×#491	C₂	semidirect
5. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#483	C₂	semidirect
7. C₂×C₇×#479	C₂	semidirect
8. C₂×C₇×#470	C₂	semidirect
9. C₂×C₇×#467	C₂	semidirect
10. C₂×C₇×#462	C₂	semidirect
11. C₂×C₇×#451	C₂	semidirect
12. C₂×C₇×#451	C₂	semidirect
13. C₂×C₇×#441	C₂	semidirect
15. C₂×C₇×#419	C₂	semidirect
16. C₂²×C₇×#103	C₂	semidirect
47. C₇×#491	C₂²	semidirect
48. C₇×#485	C₂²	semidirect
49. C₇×#483	C₂²	semidirect
50. C₇×#479	C₂²	semidirect
51. C₇×#470	C₂²	semidirect
52. C₇×#467	C₂²	semidirect
53. C₇×#462	C₂²	semidirect
54. C₇×#451	C₂²	semidirect
55. C₇×#451	C₂²	semidirect
56. C₇×#441	C₂²	semidirect
62. C₇×#419	C₂²	semidirect
73. C₂×C₇×#103	C₂²	semidirect
77. C₂×#3312	C₇	direct (N × H)
188. #3312	C₂×C₇	direct (N × H)
189. C₂×#491	C₂×C₇	semidirect
190. C₂×#485	C₂×C₇	semidirect
191. C₂×#483	C₂×C₇	semidirect
192. C₂×#479	C₂×C₇	semidirect
193. C₂×#470	C₂×C₇	semidirect
194. C₂×#467	C₂×C₇	semidirect
195. C₂×#462	C₂×C₇	semidirect
196. C₂×#451	C₂×C₇	semidirect
197. C₂×#451	C₂×C₇	semidirect
198. C₂×#441	C₂×C₇	semidirect
200. C₂×#419	C₂×C₇	semidirect
201. C₂²×#103	C₂×C₇	semidirect
334. #491	C₂²×C₇	semidirect
335. #485	C₂²×C₇	semidirect
336. #483	C₂²×C₇	semidirect
337. #479	C₂²×C₇	semidirect
338. #470	C₂²×C₇	semidirect
339. #467	C₂²×C₇	semidirect
340. #462	C₂²×C₇	semidirect
341. #451	C₂²×C₇	semidirect
342. #451	C₂²×C₇	semidirect
343. #441	C₂²×C₇	semidirect
349. #419	C₂²×C₇	semidirect
360. C₂×#103	C₂²×C₇	semidirect
668. C₂×C₇	#3312	direct (N × H)
737. C₇	C₂×#3312	direct (N × H)
767. C₂	C₇×#3312	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×#552	2
C₂×C₇×D₄×Q₈	2
C₇×#3312	2
C₂×C₇×#491	2
C₂×C₇×#485	2
C₂×C₇×#483	2
C₂×C₇×#479	2
C₂×C₇×#470	2
C₂×C₇×#467	2
C₂×C₇×#462	2
C₂×C₇×#451	2
C₂×C₇×#441	2
C₂×C₇×#435	2
C₂×C₇×#419	2
C₂²×C₇×#103	2
C₂×#3312	7

Subgroups — C2×C7×#3312 #13238347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3312 #13238347