Subgroups — C₂×C₇×#3081 #13237701

Order 1792.

2234 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#518	C₂	1	1	yes	maximal, characteristic
3	C₇×#3081	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#476	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#474	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×#102	C₂	1	1	yes	maximal, characteristic
13	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₇×#544	—	2	4	no	—
17	C₇×#544	C₂²	1	8	yes	complemented
18	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₂×C₇×#125	—	2	1	no	—
21	C₂×C₇×#125	C₂²	1	2	yes	complemented
22	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
23	C₇×#518	—	2	4	no	—
24	C₇×#518	C₂²	1	8	yes	—
25	C₂×C₄×C₇×D₄	—	2	1	no	—
26	C₂×C₄×C₇×D₄	—	2	1	no	—
27	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
28	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	C₂²	1	1	yes	characteristic
31	C₂×C₇×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₂²⋊C₄	—	2	2	no	—
34	C₇×#478	C₂²	1	16	yes	complemented
35	C₇×#478	C₂²	1	16	yes	complemented
36	C₇×#476	C₂²	1	16	yes	complemented
37	C₇×#474	C₂²	1	16	yes	complemented
38	C₇×#428	C₂²	1	8	yes	complemented
39	C₇×#427	C₂²	1	8	yes	complemented
40	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#107	C₂²	1	2	yes	complemented
43	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₇×#106	C₂²	1	2	yes	complemented
46	C₇×#424	C₂²	1	8	yes	complemented
47	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
48	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
49	C₇×#418	C₂²	1	8	yes	—
50	C₂×C₇×#102	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	2	yes	—
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×#102	C₂²	1	2	yes	—
54	C₂×C₇×#102	C₂²	1	8	yes	—
55	C₂×#3081	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁵×C₇	—	2	1	no	—
57	C₂²×C₇×Q₈	—	2	2	no	—
58	C₂²×C₇×D₄	—	2	1	no	—
59	C₂²×C₇×D₄	—	2	2	no	—
60	C₂²×C₇×D₄	—	2	4	no	—
61	C₂²×C₇×D₄	Q₈	1	8	yes	complemented
62	C₂²×C₇×D₄	C₂³	1	2	yes	—
63	C₂²×C₇×D₄	C₂³	1	4	yes	—
64	C₂³×C₄×C₇	—	2	1	no	—
65	C₂³×C₄×C₇	—	2	2	no	—
66	C₂³×C₄×C₇	—	2	2	no	—
67	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₂×C₇×M₁₆	—	2	4	no	—
69	C₂×C₇×M₁₆	C₂³	1	4	yes	—
70	C₂²×C₇×C₈	—	2	4	no	—
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	2	yes	—
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	4	yes	—
75	C₇×C₄⋊Q₈	—	2	8	no	—
76	C₇×C₄⋊Q₈	—	2	4	no	—
77	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
78	C₇×#125	—	2	8	no	—
79	C₇×#125	—	2	4	no	—
80	C₇×#125	C₂³	1	8	yes	complemented
81	C₇×C₂²⋊Q₈	—	2	16	no	—
82	C₄×C₇×D₄	—	2	8	no	—
83	C₄×C₇×D₄	—	2	8	no	—
84	C₄×C₇×D₄	—	2	4	no	—
85	C₄×C₇×D₄	—	2	4	no	—
86	C₄×C₇×D₄	C₂³	1	8	yes	—
87	C₄×C₇×D₄	C₂³	1	8	yes	—
88	C₇×#117	—	2	2	no	—
89	C₇×#117	—	2	2	no	—
90	C₇×#117	D₄	1	4	yes	—
91	C₇×#117	C₂³	1	4	yes	—
92	C₇×#117	C₂³	1	4	yes	—
93	C₇×#117	C₂³	1	4	yes	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	—	2	2	no	—
96	C₂×C₇×C₄⋊C₄	—	2	2	no	—
97	C₂×C₇×C₄⋊C₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	2	no	—
99	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
112	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
113	C₂×C₄²×C₇	—	2	1	no	—
114	C₂×C₄²×C₇	—	2	1	no	—
115	C₂×C₄²×C₇	C₂³	1	2	yes	—
116	C₇×#107	C₂³	1	4	yes	complemented
117	C₇×#107	C₂³	1	8	yes	complemented
118	C₇×#107	C₂³	1	4	yes	complemented
119	C₇×#106	C₂³	1	4	yes	complemented
120	C₇×#106	C₂³	1	8	yes	complemented
121	C₇×#106	C₂³	1	4	yes	complemented
122	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
123	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
124	C₇×#102	C₂³	1	8	yes	—
125	C₇×#102	C₂³	1	8	yes	—
126	C₇×#102	C₂³	1	8	yes	—
127	C₇×#102	C₂³	1	8	yes	—
128	C₂×#544	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂×#518	C₂×C₇	1	1	yes	characteristic
130	#3081	C₂×C₇	1	16	yes	direct product factor
131	C₂×#478	C₂×C₇	1	2	yes	complemented
132	C₂×#478	C₂×C₇	1	2	yes	complemented
133	C₂×#476	C₂×C₇	1	2	yes	complemented
134	C₂×#474	C₂×C₇	1	2	yes	complemented
135	C₂×#428	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#418	C₂×C₇	1	1	yes	characteristic
139	C₂²×#102	C₂×C₇	1	1	yes	characteristic
140	C₂⁴×C₇	—	2	2	no	—
141	C₂⁴×C₇	—	2	8	no	—
142	C₂⁴×C₇	—	2	4	no	—
143	C₂⁴×C₇	—	8	2	no	—
144	C₂⁴×C₇	—	8	2	no	—
145	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₇×Q₈	—	2	8	no	—
147	C₂×C₇×Q₈	—	8	4	no	—
148	C₂×C₇×D₄	—	2	16	no	—
149	C₂×C₇×D₄	—	2	8	no	—
150	C₂×C₇×D₄	—	2	4	no	—
151	C₂×C₇×D₄	—	2	2	no	—
152	C₂×C₇×D₄	—	2	4	no	—
153	C₂×C₇×D₄	—	2	8	no	—
154	C₂×C₇×D₄	C₂×Q₈	1	8	yes	—
155	C₂×C₇×D₄	C₂×Q₈	1	16	yes	complemented
156	C₂×C₇×D₄	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	2	no	—
162	C₂²×C₄×C₇	—	2	4	no	—
163	C₂²×C₄×C₇	—	2	8	no	—
164	C₂²×C₄×C₇	—	2	8	no	—
165	C₂²×C₄×C₇	—	8	4	no	—
166	C₂²×C₄×C₇	—	8	4	no	—
167	C₂²×C₄×C₇	—	8	2	no	—
168	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
173	C₂²×C₄×C₇	#41	1	4	yes	—
174	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
176	C₇×M₁₆	—	2	8	no	—
177	C₂×C₇×C₈	—	2	2	no	—
178	C₂×C₇×C₈	—	2	2	no	—
179	C₂×C₇×C₈	—	2	8	no	—
180	C₂×C₇×C₈	—	2	4	no	—
181	C₂×C₇×C₈	C₂⁴	1	2	yes	—
182	C₂×C₇×C₈	C₂⁴	1	4	yes	—
183	C₂×C₇×C₈	C₂⁴	1	2	yes	—
184	C₇×C₄⋊C₄	—	2	4	no	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	—	2	8	no	—
187	C₇×C₄⋊C₄	—	2	8	no	—
188	C₇×C₄⋊C₄	—	2	8	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
194	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
195	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
196	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
197	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
198	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
199	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
200	C₇×C₂²⋊C₄	—	2	4	no	—
201	C₇×C₂²⋊C₄	—	2	4	no	—
202	C₇×C₂²⋊C₄	—	2	8	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
205	C₄²×C₇	—	2	4	no	—
206	C₄²×C₇	—	2	4	no	—
207	C₄²×C₇	C₂×D₄	1	4	yes	—
208	C₄²×C₇	C₂⁴	1	4	yes	—
209	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
210	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
212	#544	—	2	4	no	—
213	#544	C₂²×C₇	1	8	yes	complemented
214	C₂×C₄⋊Q₈	—	2	1	no	—
215	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
216	C₂×#125	—	2	1	no	—
217	C₂×#125	C₂²×C₇	1	2	yes	complemented
218	C₂×C₂²⋊Q₈	—	2	2	no	—
219	#518	—	2	4	no	—
220	#518	C₂²×C₇	1	8	yes	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
224	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
225	C₂×#117	C₂²×C₇	1	1	yes	characteristic
226	C₂×#117	C₂²×C₇	1	1	yes	characteristic
227	C₂×#117	C₂²×C₇	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
229	C₂²×C₂²⋊C₄	—	2	2	no	—
230	#478	C₂²×C₇	1	16	yes	complemented
231	#478	C₂²×C₇	1	16	yes	complemented
232	#476	C₂²×C₇	1	16	yes	complemented
233	#474	C₂²×C₇	1	16	yes	complemented
234	#428	C₂²×C₇	1	8	yes	complemented
235	#427	C₂²×C₇	1	8	yes	complemented
236	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
237	C₂×#107	C₂²×C₇	1	2	yes	complemented
238	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
239	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
240	C₂×#106	C₂²×C₇	1	2	yes	complemented
241	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
242	#424	C₂²×C₇	1	8	yes	complemented
243	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
244	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
245	#418	C₂²×C₇	1	8	yes	—
246	C₂×#102	C₂²×C₇	1	2	yes	—
247	C₂×#102	C₂²×C₇	1	2	yes	—
248	C₂×#102	C₂²×C₇	1	2	yes	—
249	C₂×#102	C₂²×C₇	1	8	yes	—
250	C₂×#102	C₂²×C₇	1	2	yes	—
251	C₂³×C₇	—	2	2	no	—
252	C₂³×C₇	—	2	2	no	—
253	C₂³×C₇	—	2	8	no	—
254	C₂³×C₇	—	2	4	no	—
255	C₂³×C₇	—	2	16	no	—
256	C₂³×C₇	—	4	4	no	—
257	C₂³×C₇	—	4	4	no	—
258	C₂³×C₇	—	8	16	no	—
259	C₂³×C₇	—	8	4	no	—
260	C₂³×C₇	—	8	4	no	—
261	C₂³×C₇	C₂²⋊Q₈	1	4	yes	—
262	C₂³×C₇	C₂²×D₄	1	2	yes	—
263	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
264	C₇×Q₈	—	8	8	no	—
265	C₇×D₄	—	2	8	no	—
266	C₇×D₄	—	2	16	no	—
267	C₇×D₄	—	2	4	no	—
268	C₇×D₄	C₂²×Q₈	1	8	yes	—
269	C₂×C₄×C₇	—	2	4	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	2	no	—
275	C₂×C₄×C₇	—	2	4	no	—
276	C₂×C₄×C₇	—	4	2	no	—
277	C₂×C₄×C₇	—	4	4	no	—
278	C₂×C₄×C₇	—	4	2	no	—
279	C₂×C₄×C₇	—	4	2	no	—
280	C₂×C₄×C₇	—	4	2	no	—
281	C₂×C₄×C₇	—	8	8	no	—
282	C₂×C₄×C₇	—	8	8	no	—
283	C₂×C₄×C₇	—	8	4	no	—
284	C₂×C₄×C₇	C₂²⋊Q₈	1	8	yes	—
285	C₂×C₄×C₇	C₂²⋊Q₈	1	4	yes	—
286	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
287	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
288	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
291	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
292	C₂×C₄×C₇	C₂×#41	1	2	yes	—
293	C₂×C₄×C₇	C₂×#41	1	4	yes	—
294	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
295	C₇×C₈	—	2	2	no	—
296	C₇×C₈	—	2	2	no	—
297	C₇×C₈	—	2	4	no	—
298	C₂⁵	—	2	1	no	—
299	C₂²×Q₈	—	2	2	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	4	no	—
303	C₂²×D₄	C₇×Q₈	1	8	yes	complemented
304	C₂²×D₄	C₂³×C₇	1	2	yes	—
305	C₂²×D₄	C₂³×C₇	1	4	yes	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
310	C₂×M₁₆	—	2	4	no	—
311	C₂×M₁₆	C₂³×C₇	1	4	yes	—
312	C₂²×C₈	—	2	4	no	—
313	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₇	1	4	yes	—
316	C₂²×C₈	C₂³×C₇	1	2	yes	—
317	C₄⋊Q₈	—	2	8	no	—
318	C₄⋊Q₈	—	2	4	no	—
319	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
320	#125	—	2	8	no	—
321	#125	—	2	4	no	—
322	#125	C₂³×C₇	1	8	yes	complemented
323	C₂²⋊Q₈	—	2	16	no	—
324	C₄×D₄	—	2	8	no	—
325	C₄×D₄	—	2	8	no	—
326	C₄×D₄	—	2	4	no	—
327	C₄×D₄	—	2	4	no	—
328	C₄×D₄	C₂³×C₇	1	8	yes	—
329	C₄×D₄	C₂³×C₇	1	8	yes	—
330	#117	—	2	2	no	—
331	#117	—	2	2	no	—
332	#117	C₇×D₄	1	4	yes	—
333	#117	C₂³×C₇	1	4	yes	—
334	#117	C₂³×C₇	1	4	yes	—
335	#117	C₂³×C₇	1	4	yes	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	16	no	—
354	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	C₂³×C₇	1	2	yes	—
358	#107	C₂³×C₇	1	4	yes	complemented
359	#107	C₂³×C₇	1	4	yes	complemented
360	#107	C₂³×C₇	1	8	yes	complemented
361	#106	C₂³×C₇	1	4	yes	complemented
362	#106	C₂³×C₇	1	4	yes	complemented
363	#106	C₂³×C₇	1	8	yes	complemented
364	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
365	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
366	#102	C₂³×C₇	1	8	yes	—
367	#102	C₂³×C₇	1	8	yes	—
368	#102	C₂³×C₇	1	8	yes	—
369	#102	C₂³×C₇	1	8	yes	—
370	C₂²×C₇	—	2	8	no	—
371	C₂²×C₇	—	2	2	no	—
372	C₂²×C₇	—	2	2	no	—
373	C₂²×C₇	—	2	8	no	—
374	C₂²×C₇	—	4	16	no	—
375	C₂²×C₇	—	4	4	no	—
376	C₂²×C₇	—	4	4	no	—
377	C₂²×C₇	—	8	16	no	—
378	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
379	C₂²×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
380	C₂²×C₇	#576	1	2	yes	—
381	C₂²×C₇	#577	1	2	yes	—
382	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
383	C₄×C₇	—	2	4	no	—
384	C₄×C₇	—	2	4	no	—
385	C₄×C₇	—	4	2	no	—
386	C₄×C₇	—	4	4	no	—
387	C₄×C₇	—	4	2	no	—
388	C₄×C₇	—	4	2	no	—
389	C₄×C₇	—	4	2	no	—
390	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
391	C₄×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
392	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
393	C₄×C₇	C₂²×#41	1	1	yes	characteristic
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	2	8	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	8	2	no	—
398	C₂⁴	—	8	2	no	—
399	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
400	C₂×Q₈	—	2	8	no	—
401	C₂×Q₈	—	8	4	no	—
402	C₂×D₄	—	2	16	no	—
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	C₂×C₇×Q₈	1	8	yes	—
409	C₂×D₄	C₂×C₇×Q₈	1	16	yes	complemented
410	C₂×D₄	C₂⁴×C₇	1	4	yes	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	2	8	no	—
419	C₂²×C₄	—	8	4	no	—
420	C₂²×C₄	—	8	4	no	—
421	C₂²×C₄	—	8	2	no	—
422	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
423	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
424	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
426	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
427	C₂²×C₄	C₇×#41	1	4	yes	—
428	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
430	M₁₆	—	2	8	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	8	no	—
434	C₂×C₈	—	2	4	no	—
435	C₂×C₈	C₂⁴×C₇	1	2	yes	—
436	C₂×C₈	C₂⁴×C₇	1	4	yes	—
437	C₂×C₈	C₂⁴×C₇	1	2	yes	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
448	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
449	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
450	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
451	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
452	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
453	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
459	C₄²	—	2	4	no	—
460	C₄²	—	2	4	no	—
461	C₄²	C₂×C₇×D₄	1	4	yes	—
462	C₄²	C₂⁴×C₇	1	4	yes	—
463	C₂×C₇	—	2	4	no	—
464	C₂×C₇	—	4	8	no	—
465	C₂×C₇	#3081	1	4	yes	direct product factor
466	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
467	C₂×C₇	C₂×#576	1	1	yes	characteristic
468	C₂×C₇	C₂×#577	1	1	yes	characteristic
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	8	no	—
473	C₂³	—	2	16	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	8	4	no	—
477	C₂³	—	8	4	no	—
478	C₂³	—	8	16	no	—
479	C₂³	C₇×C₂²⋊Q₈	1	4	yes	—
480	C₂³	C₂²×C₇×D₄	1	2	yes	—
481	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
482	Q₈	—	8	8	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	8	no	—
485	D₄	—	2	16	no	—
486	D₄	C₂²×C₇×Q₈	1	8	yes	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	8	8	no	—
500	C₂×C₄	—	8	8	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	C₇×C₂²⋊Q₈	1	8	yes	—
503	C₂×C₄	C₇×C₂²⋊Q₈	1	4	yes	—
504	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
505	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
506	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
507	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
508	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
509	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
510	C₂×C₄	C₂×C₇×#41	1	2	yes	—
511	C₂×C₄	C₂×C₇×#41	1	4	yes	—
512	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
513	C₈	—	2	2	no	—
514	C₈	—	2	2	no	—
515	C₈	—	2	4	no	—
516	C₇	C₂×#3081	1	1	yes	characteristic, direct product factor, Sylow
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	8	no	—
520	C₂²	—	2	8	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	16	no	—
524	C₂²	—	8	16	no	—
525	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
526	C₂²	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
527	C₂²	C₇×#576	1	2	yes	—
528	C₂²	C₇×#577	1	2	yes	—
529	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	4	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
538	C₄	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
539	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
540	C₄	C₂²×C₇×#41	1	1	yes	characteristic
541	C₂	—	2	4	no	—
542	C₂	—	4	8	no	—
543	C₂	C₇×#3081	1	4	yes	direct product factor
544	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
545	C₂	C₂×C₇×#576	1	1	yes	characteristic
546	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	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
1. C₂×C₇×#544	C₂	semidirect
3. C₇×#3081	C₂	direct (N × H)
4. C₂×C₇×#478	C₂	semidirect
5. C₂×C₇×#478	C₂	semidirect
6. C₂×C₇×#476	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
8. C₂×C₇×#428	C₂	semidirect
9. C₂×C₇×#427	C₂	semidirect
10. C₂×C₇×#424	C₂	semidirect
17. C₇×#544	C₂²	semidirect
19. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₇×#125	C₂²	semidirect
34. C₇×#478	C₂²	semidirect
35. C₇×#478	C₂²	semidirect
36. C₇×#476	C₂²	semidirect
37. C₇×#474	C₂²	semidirect
38. C₇×#428	C₂²	semidirect
39. C₇×#427	C₂²	semidirect
40. C₂×C₇×#107	C₂²	semidirect
41. C₂×C₇×#107	C₂²	semidirect
42. C₂×C₇×#107	C₂²	semidirect
43. C₂×C₇×#106	C₂²	semidirect
44. C₂×C₇×#106	C₂²	semidirect
45. C₂×C₇×#106	C₂²	semidirect
46. C₇×#424	C₂²	semidirect
47. C₂×C₇×C₄⋊C₈	C₂²	semidirect
48. C₂×C₇×C₄⋊C₈	C₂²	semidirect
55. C₂×#3081	C₇	direct (N × H)
61. C₂²×C₇×D₄	Q₈	semidirect
77. C₇×C₄⋊Q₈	C₂³	semidirect
80. C₇×#125	C₂³	semidirect
116. C₇×#107	C₂³	semidirect
117. C₇×#107	C₂³	semidirect
118. C₇×#107	C₂³	semidirect
119. C₇×#106	C₂³	semidirect
120. C₇×#106	C₂³	semidirect
121. C₇×#106	C₂³	semidirect
122. C₇×C₄⋊C₈	C₂³	semidirect
123. C₇×C₄⋊C₈	C₂³	semidirect
128. C₂×#544	C₂×C₇	semidirect
130. #3081	C₂×C₇	direct (N × H)
131. C₂×#478	C₂×C₇	semidirect
132. C₂×#478	C₂×C₇	semidirect
133. C₂×#476	C₂×C₇	semidirect
134. C₂×#474	C₂×C₇	semidirect
135. C₂×#428	C₂×C₇	semidirect
136. C₂×#427	C₂×C₇	semidirect
137. C₂×#424	C₂×C₇	semidirect
155. C₂×C₇×D₄	C₂×Q₈	semidirect
213. #544	C₂²×C₇	semidirect
215. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
217. C₂×#125	C₂²×C₇	semidirect
230. #478	C₂²×C₇	semidirect
231. #478	C₂²×C₇	semidirect
232. #476	C₂²×C₇	semidirect
233. #474	C₂²×C₇	semidirect
234. #428	C₂²×C₇	semidirect
235. #427	C₂²×C₇	semidirect
236. C₂×#107	C₂²×C₇	semidirect
237. C₂×#107	C₂²×C₇	semidirect
238. C₂×#107	C₂²×C₇	semidirect
239. C₂×#106	C₂²×C₇	semidirect
240. C₂×#106	C₂²×C₇	semidirect
241. C₂×#106	C₂²×C₇	semidirect
242. #424	C₂²×C₇	semidirect
243. C₂×C₄⋊C₈	C₂²×C₇	semidirect
244. C₂×C₄⋊C₈	C₂²×C₇	semidirect
303. C₂²×D₄	C₇×Q₈	semidirect
319. C₄⋊Q₈	C₂³×C₇	semidirect
322. #125	C₂³×C₇	semidirect
358. #107	C₂³×C₇	semidirect
359. #107	C₂³×C₇	semidirect
360. #107	C₂³×C₇	semidirect
361. #106	C₂³×C₇	semidirect
362. #106	C₂³×C₇	semidirect
363. #106	C₂³×C₇	semidirect
364. C₄⋊C₈	C₂³×C₇	semidirect
365. C₄⋊C₈	C₂³×C₇	semidirect
409. C₂×D₄	C₂×C₇×Q₈	semidirect
465. C₂×C₇	#3081	direct (N × H)
516. C₇	C₂×#3081	direct (N × H)
543. C₂	C₇×#3081	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×#544	2
C₂×C₇×#518	2
C₇×#3081	2
C₂×C₇×#478	2
C₂×C₇×#476	2
C₂×C₇×#474	2
C₂×C₇×#428	2
C₂×C₇×#427	2
C₂×C₇×#424	2
C₂×C₇×#418	2
C₂²×C₇×#102	2
C₂×#3081	7

Subgroups — C2×C7×#3081 #13237701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3081 #13237701