Subgroups — C₂×C₇×#3114 #13237753

Order 1792.

2582 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3114	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#463	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#447	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×#442	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₇	—	2	1	no	—
15	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₇×D₈	C₂²	1	2	yes	—
17	C₇×#529	—	2	4	no	—
18	C₇×#529	C₂²	1	8	yes	complemented
19	C₂×C₇×#126	—	2	1	no	—
20	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₇×#123	—	2	1	no	—
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×C₇×D₄	—	2	1	no	—
27	C₂×C₄×C₇×D₄	—	2	1	no	—
28	C₂×C₄×C₇×D₄	—	2	1	no	—
29	C₂×C₄×C₇×D₄	—	2	4	no	—
30	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
33	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₇×#117	—	2	1	no	—
35	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
37	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
38	C₇×#483	C₂²	1	8	yes	complemented
39	C₇×#480	C₂²	1	8	yes	complemented
40	C₇×#478	C₂²	1	16	yes	complemented
41	C₇×#463	C₂²	1	16	yes	complemented
42	C₇×#450	C₂²	1	8	yes	complemented
43	C₇×#447	C₂²	1	8	yes	—
44	C₇×#442	C₂²	1	16	yes	complemented
45	C₇×#440	C₂²	1	16	yes	complemented
46	C₇×#432	C₂²	1	8	yes	complemented
47	C₂×C₇×#107	C₂²	1	2	yes	complemented
48	C₂×C₇×#106	C₂²	1	2	yes	complemented
49	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
50	C₂×C₇×#103	C₂²	1	2	yes	complemented
51	C₂×C₇×#102	C₂²	1	2	yes	—
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×#102	C₂²	1	2	yes	complemented
54	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₇×#97	C₂²	1	2	yes	complemented
57	C₂×#3114	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂⁵×C₇	—	2	1	no	—
59	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
60	C₂²×C₇×D₄	—	2	8	no	—
61	C₂²×C₇×D₄	—	2	1	no	—
62	C₂²×C₇×D₄	—	2	2	no	—
63	C₂²×C₇×D₄	—	2	1	no	—
64	C₂²×C₇×D₄	C₂³	1	4	yes	—
65	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂³	1	2	yes	—
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	—	2	2	no	—
70	C₂³×C₄×C₇	—	2	2	no	—
71	C₂³×C₄×C₇	—	2	8	no	—
72	C₂³×C₄×C₇	—	4	8	no	—
73	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₇×SD₁₆	—	2	8	no	—
77	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
78	C₂×C₇×D₈	—	2	8	no	—
79	C₂×C₇×D₈	C₂³	1	8	yes	—
80	C₂²×C₇×C₈	C₂³	1	2	yes	—
81	C₂²×C₇×C₈	C₂³	1	2	yes	—
82	C₇×#126	—	2	8	no	—
83	C₇×#125	—	2	2	no	—
84	C₇×#125	C₂³	1	4	yes	complemented
85	C₇×#124	—	2	2	no	—
86	C₇×#124	C₂³	1	4	yes	complemented
87	C₇×#123	—	2	8	no	—
88	C₇×C₂²⋊Q₈	—	2	2	no	—
89	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
90	C₇×#121	—	2	2	no	—
91	C₇×#121	C₂³	1	4	yes	—
92	C₄×C₇×Q₈	—	2	2	no	—
93	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
94	C₄×C₇×D₄	—	2	8	no	—
95	C₄×C₇×D₄	—	2	4	no	—
96	C₄×C₇×D₄	—	2	4	no	—
97	C₄×C₇×D₄	—	2	8	no	—
98	C₄×C₇×D₄	—	2	8	no	—
99	C₄×C₇×D₄	—	2	2	no	—
100	C₄×C₇×D₄	C₂³	1	8	yes	—
101	C₄×C₇×D₄	C₂³	1	8	yes	—
102	C₄×C₇×D₄	C₂³	1	4	yes	complemented
103	C₇×#117	—	2	8	no	—
104	C₂×C₇×C₄⋊C₄	—	2	2	no	—
105	C₂×C₇×C₄⋊C₄	—	2	1	no	—
106	C₂×C₇×C₄⋊C₄	—	2	1	no	—
107	C₂×C₇×C₄⋊C₄	—	2	1	no	—
108	C₂×C₇×C₄⋊C₄	—	2	1	no	—
109	C₂×C₇×C₄⋊C₄	—	2	1	no	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
118	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₄²×C₇	—	2	1	no	—
123	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₇	D₄	1	4	yes	—
126	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇	C₂³	1	4	yes	—
129	C₇×#107	C₂³	1	8	yes	complemented
130	C₇×#106	C₂³	1	8	yes	complemented
131	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
132	C₇×#103	C₂³	1	8	yes	complemented
133	C₇×#102	C₂³	1	8	yes	—
134	C₇×#102	C₂³	1	8	yes	—
135	C₇×#102	C₂³	1	8	yes	complemented
136	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
137	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
138	C₇×#97	C₂³	1	8	yes	complemented
139	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
141	#3114	C₂×C₇	1	16	yes	direct product factor
142	C₂×#483	C₂×C₇	1	1	yes	characteristic, complemented
143	C₂×#480	C₂×C₇	1	1	yes	characteristic, complemented
144	C₂×#478	C₂×C₇	1	2	yes	complemented
145	C₂×#463	C₂×C₇	1	2	yes	complemented
146	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#447	C₂×C₇	1	1	yes	characteristic
148	C₂×#442	C₂×C₇	1	2	yes	complemented
149	C₂×#440	C₂×C₇	1	2	yes	complemented
150	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
151	C₂⁴×C₇	—	2	8	no	—
152	C₂⁴×C₇	—	2	4	no	—
153	C₂⁴×C₇	—	2	2	no	—
154	C₂⁴×C₇	—	2	1	no	—
155	C₂⁴×C₇	—	4	4	no	—
156	C₂⁴×C₇	—	4	4	no	—
157	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂×C₇×Q₈	—	2	1	no	—
159	C₂×C₇×Q₈	—	2	4	no	—
160	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
161	C₂×C₇×D₄	—	2	8	no	—
162	C₂×C₇×D₄	—	2	16	no	—
163	C₂×C₇×D₄	—	2	16	no	—
164	C₂×C₇×D₄	—	2	4	no	—
165	C₂×C₇×D₄	—	2	4	no	—
166	C₂×C₇×D₄	—	2	2	no	—
167	C₂×C₇×D₄	—	2	1	no	—
168	C₂×C₇×D₄	—	2	4	no	—
169	C₂×C₇×D₄	—	2	4	no	—
170	C₂×C₇×D₄	—	4	4	no	—
171	C₂×C₇×D₄	#41	1	8	yes	—
172	C₂×C₇×D₄	C₂⁴	1	2	yes	—
173	C₂×C₇×D₄	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₇	—	2	4	no	—
175	C₂²×C₄×C₇	—	2	4	no	—
176	C₂²×C₄×C₇	—	2	4	no	—
177	C₂²×C₄×C₇	—	2	1	no	—
178	C₂²×C₄×C₇	—	2	1	no	—
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	2	2	no	—
181	C₂²×C₄×C₇	—	2	4	no	—
182	C₂²×C₄×C₇	—	2	8	no	—
183	C₂²×C₄×C₇	—	2	8	no	—
184	C₂²×C₄×C₇	—	4	2	no	—
185	C₂²×C₄×C₇	—	4	4	no	—
186	C₂²×C₄×C₇	—	4	8	no	—
187	C₂²×C₄×C₇	—	4	8	no	—
188	C₂²×C₄×C₇	—	4	32	no	—
189	C₂²×C₄×C₇	—	4	4	no	—
190	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
200	C₇×SD₁₆	—	2	16	no	—
201	C₇×D₈	—	2	16	no	—
202	C₂×C₇×C₈	—	2	4	no	—
203	C₂×C₇×C₈	—	2	4	no	—
204	C₂×C₇×C₈	C₂⁴	1	4	yes	—
205	C₂×C₇×C₈	C₂⁴	1	4	yes	—
206	C₇×C₄⋊C₄	—	2	4	no	—
207	C₇×C₄⋊C₄	—	2	2	no	—
208	C₇×C₄⋊C₄	—	2	4	no	—
209	C₇×C₄⋊C₄	—	2	4	no	—
210	C₇×C₄⋊C₄	—	2	4	no	—
211	C₇×C₄⋊C₄	—	2	4	no	—
212	C₇×C₄⋊C₄	—	2	1	no	—
213	C₇×C₄⋊C₄	—	2	1	no	—
214	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
215	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
216	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
217	C₇×C₂²⋊C₄	—	2	4	no	—
218	C₇×C₂²⋊C₄	—	2	8	no	—
219	C₇×C₂²⋊C₄	—	2	8	no	—
220	C₇×C₂²⋊C₄	—	2	4	no	—
221	C₇×C₂²⋊C₄	—	2	4	no	—
222	C₇×C₂²⋊C₄	—	2	4	no	—
223	C₇×C₂²⋊C₄	—	2	4	no	—
224	C₄²×C₇	—	2	4	no	—
225	C₄²×C₇	C₂×D₄	1	4	yes	—
226	C₄²×C₇	C₂×D₄	1	2	yes	—
227	C₄²×C₇	C₂×D₄	1	2	yes	—
228	C₄²×C₇	C₂×D₄	1	4	yes	—
229	C₄²×C₇	C₂⁴	1	2	yes	—
230	C₄²×C₇	C₂⁴	1	2	yes	—
231	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
232	C₂⁴×C₄	—	2	1	no	—
233	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
234	C₂²×D₈	C₂²×C₇	1	2	yes	—
235	#529	—	2	4	no	—
236	#529	C₂²×C₇	1	8	yes	complemented
237	C₂×#126	—	2	1	no	—
238	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
239	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
240	C₂×#123	—	2	1	no	—
241	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
242	C₂×#121	C₂²×C₇	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
244	C₂×C₄×D₄	—	2	1	no	—
245	C₂×C₄×D₄	—	2	1	no	—
246	C₂×C₄×D₄	—	2	1	no	—
247	C₂×C₄×D₄	—	2	4	no	—
248	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
250	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
251	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
252	C₂×#117	—	2	1	no	—
253	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	—	2	1	no	—
255	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
256	#483	C₂²×C₇	1	8	yes	complemented
257	#480	C₂²×C₇	1	8	yes	complemented
258	#478	C₂²×C₇	1	16	yes	complemented
259	#463	C₂²×C₇	1	16	yes	complemented
260	#450	C₂²×C₇	1	8	yes	complemented
261	#447	C₂²×C₇	1	8	yes	—
262	#442	C₂²×C₇	1	16	yes	complemented
263	#440	C₂²×C₇	1	16	yes	complemented
264	#432	C₂²×C₇	1	8	yes	complemented
265	C₂×#107	C₂²×C₇	1	2	yes	complemented
266	C₂×#106	C₂²×C₇	1	2	yes	complemented
267	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
268	C₂×#103	C₂²×C₇	1	2	yes	complemented
269	C₂×#102	C₂²×C₇	1	2	yes	—
270	C₂×#102	C₂²×C₇	1	2	yes	—
271	C₂×#102	C₂²×C₇	1	2	yes	complemented
272	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
274	C₂×#97	C₂²×C₇	1	2	yes	complemented
275	C₂³×C₇	—	2	2	no	—
276	C₂³×C₇	—	2	2	no	—
277	C₂³×C₇	—	2	16	no	—
278	C₂³×C₇	—	2	8	no	—
279	C₂³×C₇	—	2	4	no	—
280	C₂³×C₇	—	2	2	no	—
281	C₂³×C₇	—	4	32	no	—
282	C₂³×C₇	—	4	8	no	—
283	C₂³×C₇	—	4	8	no	—
284	C₂³×C₇	—	4	4	no	—
285	C₂³×C₇	—	4	4	no	—
286	C₂³×C₇	—	4	2	no	—
287	C₂³×C₇	—	4	2	no	—
288	C₂³×C₇	—	4	2	no	—
289	C₂³×C₇	AGL(1,ℤ/8)	1	4	yes	—
290	C₂³×C₇	C₂²×D₄	1	2	yes	—
291	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
292	C₇×Q₈	—	2	4	no	—
293	C₇×Q₈	—	4	2	no	—
294	C₇×D₄	—	2	16	no	—
295	C₇×D₄	—	2	8	no	—
296	C₇×D₄	—	2	4	no	—
297	C₇×D₄	—	2	4	no	—
298	C₇×D₄	—	4	8	no	—
299	C₇×D₄	—	4	2	no	—
300	C₇×D₄	C₂×#41	1	8	yes	—
301	C₂×C₄×C₇	—	2	2	no	—
302	C₂×C₄×C₇	—	2	8	no	—
303	C₂×C₄×C₇	—	2	2	no	—
304	C₂×C₄×C₇	—	2	2	no	—
305	C₂×C₄×C₇	—	2	2	no	—
306	C₂×C₄×C₇	—	2	2	no	—
307	C₂×C₄×C₇	—	2	4	no	—
308	C₂×C₄×C₇	—	2	4	no	—
309	C₂×C₄×C₇	—	2	2	no	—
310	C₂×C₄×C₇	—	2	2	no	—
311	C₂×C₄×C₇	—	2	2	no	—
312	C₂×C₄×C₇	—	2	4	no	—
313	C₂×C₄×C₇	—	4	4	no	—
314	C₂×C₄×C₇	—	4	8	no	—
315	C₂×C₄×C₇	—	4	16	no	—
316	C₂×C₄×C₇	—	4	16	no	—
317	C₂×C₄×C₇	—	4	2	no	—
318	C₂×C₄×C₇	—	4	8	no	—
319	C₂×C₄×C₇	—	4	4	no	—
320	C₂×C₄×C₇	—	4	2	no	—
321	C₂×C₄×C₇	—	4	2	no	—
322	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₇	C₂×#41	1	4	yes	—
329	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
330	C₇×C₈	—	2	4	no	—
331	C₇×C₈	—	2	4	no	—
332	C₂⁵	—	2	1	no	—
333	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
334	C₂²×D₄	—	2	8	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	—	2	2	no	—
338	C₂²×D₄	C₂³×C₇	1	4	yes	—
339	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
340	C₂²×D₄	C₂³×C₇	1	2	yes	—
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	—	2	8	no	—
346	C₂³×C₄	—	4	8	no	—
347	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
348	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
350	C₂×SD₁₆	—	2	8	no	—
351	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
352	C₂×D₈	—	2	8	no	—
353	C₂×D₈	C₂³×C₇	1	8	yes	—
354	C₂²×C₈	C₂³×C₇	1	2	yes	—
355	C₂²×C₈	C₂³×C₇	1	2	yes	—
356	#126	—	2	8	no	—
357	#125	—	2	2	no	—
358	#125	C₂³×C₇	1	4	yes	complemented
359	#124	—	2	2	no	—
360	#124	C₂³×C₇	1	4	yes	complemented
361	#123	—	2	8	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
364	#121	—	2	2	no	—
365	#121	C₂³×C₇	1	4	yes	—
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
368	C₄×D₄	—	2	8	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	8	no	—
372	C₄×D₄	—	2	8	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	C₂³×C₇	1	8	yes	—
375	C₄×D₄	C₂³×C₇	1	8	yes	—
376	C₄×D₄	C₂³×C₇	1	4	yes	complemented
377	#117	—	2	8	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	8	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
398	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
399	C₂×C₄²	C₇×D₄	1	4	yes	—
400	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₇	1	4	yes	—
403	#107	C₂³×C₇	1	8	yes	complemented
404	#106	C₂³×C₇	1	8	yes	complemented
405	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
406	#103	C₂³×C₇	1	8	yes	complemented
407	#102	C₂³×C₇	1	8	yes	—
408	#102	C₂³×C₇	1	8	yes	—
409	#102	C₂³×C₇	1	8	yes	complemented
410	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
411	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
412	#97	C₂³×C₇	1	8	yes	complemented
413	C₂²×C₇	—	2	8	no	—
414	C₂²×C₇	—	2	2	no	—
415	C₂²×C₇	—	2	2	no	—
416	C₂²×C₇	—	2	8	no	—
417	C₂²×C₇	—	4	32	no	—
418	C₂²×C₇	—	4	16	no	—
419	C₂²×C₇	—	4	4	no	—
420	C₂²×C₇	—	4	4	no	—
421	C₂²×C₇	—	4	2	no	—
422	C₂²×C₇	—	4	2	no	—
423	C₂²×C₇	—	4	2	no	—
424	C₂²×C₇	—	8	4	no	—
425	C₂²×C₇	#525	1	2	yes	—
426	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
427	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
428	C₂²×C₇	#575	1	2	yes	—
429	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
430	C₄×C₇	—	2	2	no	—
431	C₄×C₇	—	2	2	no	—
432	C₄×C₇	—	2	2	no	—
433	C₄×C₇	—	2	2	no	—
434	C₄×C₇	—	2	2	no	—
435	C₄×C₇	—	4	2	no	—
436	C₄×C₇	—	4	4	no	—
437	C₄×C₇	—	4	2	no	—
438	C₄×C₇	—	4	2	no	—
439	C₄×C₇	#525	1	2	yes	—
440	C₄×C₇	C₂²×#41	1	2	yes	—
441	C₂⁴	—	2	8	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	1	no	—
445	C₂⁴	—	4	4	no	—
446	C₂⁴	—	4	4	no	—
447	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	16	no	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	C₇×#41	1	8	yes	—
462	C₂×D₄	C₂⁴×C₇	1	2	yes	—
463	C₂×D₄	C₂⁴×C₇	1	4	yes	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	8	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	8	no	—
476	C₂²×C₄	—	4	8	no	—
477	C₂²×C₄	—	4	32	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
483	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
486	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
487	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
490	SD₁₆	—	2	16	no	—
491	D₈	—	2	16	no	—
492	C₂×C₈	—	2	4	no	—
493	C₂×C₈	—	2	4	no	—
494	C₂×C₈	C₂⁴×C₇	1	4	yes	—
495	C₂×C₈	C₂⁴×C₇	1	4	yes	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
505	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
506	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₄²	—	2	4	no	—
515	C₄²	C₂×C₇×D₄	1	4	yes	—
516	C₄²	C₂×C₇×D₄	1	2	yes	—
517	C₄²	C₂×C₇×D₄	1	2	yes	—
518	C₄²	C₂×C₇×D₄	1	4	yes	—
519	C₄²	C₂⁴×C₇	1	2	yes	—
520	C₄²	C₂⁴×C₇	1	2	yes	—
521	C₂×C₇	—	2	4	no	—
522	C₂×C₇	—	4	8	no	—
523	C₂×C₇	—	8	2	no	—
524	C₂×C₇	#3114	1	4	yes	direct product factor
525	C₂×C₇	C₂×#525	1	1	yes	characteristic
526	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
527	C₂×C₇	C₂×#575	1	1	yes	characteristic
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	16	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	8	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	4	8	no	—
535	C₂³	—	4	32	no	—
536	C₂³	—	4	8	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	4	2	no	—
541	C₂³	—	4	2	no	—
542	C₂³	C₇×AGL(1,ℤ/8)	1	4	yes	—
543	C₂³	C₂²×C₇×D₄	1	2	yes	—
544	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
545	Q₈	—	2	4	no	—
546	Q₈	—	4	2	no	—
547	D₄	—	2	16	no	—
548	D₄	—	2	4	no	—
549	D₄	—	2	4	no	—
550	D₄	—	2	8	no	—
551	D₄	—	4	8	no	—
552	D₄	—	4	2	no	—
553	D₄	C₂×C₇×#41	1	8	yes	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	8	no	—
568	C₂×C₄	—	4	16	no	—
569	C₂×C₄	—	4	16	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	8	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
576	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
577	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
578	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
579	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
580	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
581	C₂×C₄	C₂×C₇×#41	1	4	yes	—
582	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
583	C₈	—	2	4	no	—
584	C₈	—	2	4	no	—
585	C₇	C₂×#3114	1	1	yes	characteristic, direct product factor, Sylow
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	8	no	—
589	C₂²	—	2	8	no	—
590	C₂²	—	4	32	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	16	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	8	4	no	—
598	C₂²	C₇×#525	1	2	yes	—
599	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
600	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
601	C₂²	C₇×#575	1	2	yes	—
602	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	4	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	C₇×#525	1	2	yes	—
613	C₄	C₂²×C₇×#41	1	2	yes	—
614	C₂	—	2	4	no	—
615	C₂	—	4	8	no	—
616	C₂	—	8	2	no	—
617	C₂	C₇×#3114	1	4	yes	direct product factor
618	C₂	C₂×C₇×#525	1	1	yes	characteristic
619	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
620	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#447	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#529	C₂	semidirect
2. C₂²×C₄×C₇×D₄	C₂	semidirect
3. C₇×#3114	C₂	direct (N × H)
4. C₂×C₇×#483	C₂	semidirect
5. C₂×C₇×#480	C₂	semidirect
6. C₂×C₇×#478	C₂	semidirect
7. C₂×C₇×#463	C₂	semidirect
8. C₂×C₇×#450	C₂	semidirect
10. C₂×C₇×#442	C₂	semidirect
11. C₂×C₇×#440	C₂	semidirect
12. C₂×C₇×#432	C₂	semidirect
18. C₇×#529	C₂²	semidirect
20. C₂×C₇×#125	C₂²	semidirect
21. C₂×C₇×#124	C₂²	semidirect
25. C₂×C₄×C₇×Q₈	C₂²	semidirect
32. C₂×C₄×C₇×D₄	C₂²	semidirect
33. C₂×C₄×C₇×D₄	C₂²	semidirect
38. C₇×#483	C₂²	semidirect
39. C₇×#480	C₂²	semidirect
40. C₇×#478	C₂²	semidirect
41. C₇×#463	C₂²	semidirect
42. C₇×#450	C₂²	semidirect
44. C₇×#442	C₂²	semidirect
45. C₇×#440	C₂²	semidirect
46. C₇×#432	C₂²	semidirect
47. C₂×C₇×#107	C₂²	semidirect
48. C₂×C₇×#106	C₂²	semidirect
49. C₂×C₇×C₄⋊C₈	C₂²	semidirect
50. C₂×C₇×#103	C₂²	semidirect
53. C₂×C₇×#102	C₂²	semidirect
56. C₂×C₇×#97	C₂²	semidirect
57. C₂×#3114	C₇	direct (N × H)
84. C₇×#125	C₂³	semidirect
86. C₇×#124	C₂³	semidirect
93. C₄×C₇×Q₈	C₂³	semidirect
102. C₄×C₇×D₄	C₂³	semidirect
129. C₇×#107	C₂³	semidirect
130. C₇×#106	C₂³	semidirect
131. C₇×C₄⋊C₈	C₂³	semidirect
132. C₇×#103	C₂³	semidirect
135. C₇×#102	C₂³	semidirect
138. C₇×#97	C₂³	semidirect
139. C₂×#529	C₂×C₇	semidirect
140. C₂²×C₄×D₄	C₂×C₇	semidirect
141. #3114	C₂×C₇	direct (N × H)
142. C₂×#483	C₂×C₇	semidirect
143. C₂×#480	C₂×C₇	semidirect
144. C₂×#478	C₂×C₇	semidirect
145. C₂×#463	C₂×C₇	semidirect
146. C₂×#450	C₂×C₇	semidirect
148. C₂×#442	C₂×C₇	semidirect
149. C₂×#440	C₂×C₇	semidirect
150. C₂×#432	C₂×C₇	semidirect
236. #529	C₂²×C₇	semidirect
238. C₂×#125	C₂²×C₇	semidirect
239. C₂×#124	C₂²×C₇	semidirect
243. C₂×C₄×Q₈	C₂²×C₇	semidirect
250. C₂×C₄×D₄	C₂²×C₇	semidirect
251. C₂×C₄×D₄	C₂²×C₇	semidirect
256. #483	C₂²×C₇	semidirect
257. #480	C₂²×C₇	semidirect
258. #478	C₂²×C₇	semidirect
259. #463	C₂²×C₇	semidirect
260. #450	C₂²×C₇	semidirect
262. #442	C₂²×C₇	semidirect
263. #440	C₂²×C₇	semidirect
264. #432	C₂²×C₇	semidirect
265. C₂×#107	C₂²×C₇	semidirect
266. C₂×#106	C₂²×C₇	semidirect
267. C₂×C₄⋊C₈	C₂²×C₇	semidirect
268. C₂×#103	C₂²×C₇	semidirect
271. C₂×#102	C₂²×C₇	semidirect
274. C₂×#97	C₂²×C₇	semidirect
358. #125	C₂³×C₇	semidirect
360. #124	C₂³×C₇	semidirect
367. C₄×Q₈	C₂³×C₇	semidirect
376. C₄×D₄	C₂³×C₇	semidirect
403. #107	C₂³×C₇	semidirect
404. #106	C₂³×C₇	semidirect
405. C₄⋊C₈	C₂³×C₇	semidirect
406. #103	C₂³×C₇	semidirect
409. #102	C₂³×C₇	semidirect
412. #97	C₂³×C₇	semidirect
524. C₂×C₇	#3114	direct (N × H)
585. C₇	C₂×#3114	direct (N × H)
617. C₂	C₇×#3114	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×#529	2
C₂²×C₄×C₇×D₄	2
C₇×#3114	2
C₂×C₇×#483	2
C₂×C₇×#480	2
C₂×C₇×#478	2
C₂×C₇×#463	2
C₂×C₇×#450	2
C₂×C₇×#447	2
C₂×C₇×#442	2
C₂×C₇×#440	2
C₂×C₇×#432	2
C₂×#3114	7

Subgroups — C2×C7×#3114 #13237753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3114 #13237753