Subgroups — C₂×C₇×#3096 #13237728

Order 1792.

2362 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3096	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#481	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#480	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×#418	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
17	C₇×#535	—	2	4	no	—
18	C₇×#535	C₂²	1	8	yes	—
19	C₂×C₇×#127	—	2	1	no	—
20	C₂×C₇×#124	—	2	1	no	—
21	C₂×C₇×#121	C₂²	1	2	yes	—
22	C₂×C₇×#121	C₂²	1	2	yes	—
23	C₂×C₇×#120	—	2	2	no	—
24	C₇×#520	—	2	4	no	—
25	C₇×#520	C₂²	1	8	yes	complemented
26	C₂×C₄×C₇×Q₈	—	2	1	no	—
27	C₂×C₄×C₇×D₄	—	2	1	no	—
28	C₂×C₄×C₇×D₄	—	2	2	no	—
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	C₂²	1	1	yes	characteristic
31	C₂×C₇×#117	C₂²	1	2	yes	complemented
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
34	C₇×#482	C₂²	1	16	yes	complemented
35	C₇×#482	C₂²	1	16	yes	complemented
36	C₇×#481	C₂²	1	16	yes	complemented
37	C₇×#480	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×#418	C₂²	1	8	yes	complemented
47	C₂×C₇×#102	C₂²	1	2	yes	—
48	C₂×C₇×#102	C₂²	1	2	yes	—
49	C₂×C₇×#102	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	8	yes	complemented
52	C₇×#408	C₂²	1	8	yes	complemented
53	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
54	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
55	C₂×#3096	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁵×C₇	—	2	1	no	—
57	C₂×C₇×#41	—	2	4	no	—
58	C₂×C₇×#41	—	2	4	no	—
59	C₂×C₇×#41	D₄	1	4	yes	—
60	C₂×C₇×#41	C₂³	1	4	yes	—
61	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
62	C₂²×C₇×D₄	—	2	2	no	—
63	C₂²×C₇×D₄	—	2	2	no	—
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	—	2	2	no	—
66	C₂²×C₇×D₄	—	2	4	no	—
67	C₂²×C₇×D₄	—	2	4	no	—
68	C₂²×C₇×D₄	D₄	1	2	yes	—
69	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
70	C₂²×C₇×D₄	C₂³	1	2	yes	—
71	C₂²×C₇×D₄	C₂³	1	4	yes	—
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	—	2	2	no	—
74	C₂³×C₄×C₇	C₂³	1	2	yes	—
75	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₇×M₁₆	—	2	4	no	—
77	C₂×C₇×M₁₆	C₂³	1	4	yes	—
78	C₂²×C₇×C₈	—	2	4	no	—
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	2	yes	—
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	4	yes	—
83	C₇×#127	—	2	8	no	—
84	C₇×#124	—	2	8	no	—
85	C₇×#121	—	2	4	no	—
86	C₇×#121	—	2	4	no	—
87	C₇×#121	C₂³	1	8	yes	—
88	C₇×#121	C₂³	1	8	yes	—
89	C₇×#120	—	2	16	no	—
90	C₄×C₇×Q₈	—	2	8	no	—
91	C₄×C₇×D₄	—	2	8	no	—
92	C₄×C₇×D₄	—	2	16	no	—
93	C₇×#117	—	2	2	no	—
94	C₇×#117	—	2	2	no	—
95	C₇×#117	—	2	4	no	—
96	C₇×#117	C₂³	1	4	yes	—
97	C₇×#117	C₂³	1	4	yes	—
98	C₇×#117	C₂³	1	8	yes	complemented
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	2	no	—
101	C₂×C₇×C₄⋊C₄	—	2	2	no	—
102	C₂×C₇×C₄⋊C₄	—	2	4	no	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₄²×C₇	—	2	1	no	—
116	C₂×C₄²×C₇	—	2	1	no	—
117	C₂×C₄²×C₇	—	2	2	no	—
118	C₇×#107	C₂³	1	4	yes	complemented
119	C₇×#107	C₂³	1	8	yes	complemented
120	C₇×#107	C₂³	1	4	yes	complemented
121	C₇×#106	C₂³	1	4	yes	complemented
122	C₇×#106	C₂³	1	8	yes	complemented
123	C₇×#106	C₂³	1	4	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	C₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
129	C₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
130	C₂×#535	C₂×C₇	1	1	yes	characteristic
131	C₂×#520	C₂×C₇	1	1	yes	characteristic, complemented
132	#3096	C₂×C₇	1	16	yes	direct product factor
133	C₂×#481	C₂×C₇	1	2	yes	complemented
134	C₂×#482	C₂×C₇	1	2	yes	complemented
135	C₂×#482	C₂×C₇	1	2	yes	complemented
136	C₂×#480	C₂×C₇	1	2	yes	complemented
137	C₂×#428	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂×#418	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂²×#102	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×#408	C₂×C₇	1	1	yes	characteristic, complemented
142	C₂⁴×C₇	—	2	2	no	—
143	C₂⁴×C₇	—	2	4	no	—
144	C₂⁴×C₇	—	4	4	no	—
145	C₂⁴×C₇	—	8	2	no	—
146	C₂⁴×C₇	—	8	2	no	—
147	C₂⁴×C₇	C₂×D₄	1	2	yes	—
148	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
149	C₇×#41	—	2	16	no	—
150	C₇×#41	—	2	8	no	—
151	C₇×#41	—	2	8	no	—
152	C₂×C₇×Q₈	—	2	4	no	—
153	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
154	C₂×C₇×D₄	—	2	8	no	—
155	C₂×C₇×D₄	—	2	8	no	—
156	C₂×C₇×D₄	—	2	8	no	—
157	C₂×C₇×D₄	—	2	4	no	—
158	C₂×C₇×D₄	—	2	2	no	—
159	C₂×C₇×D₄	—	2	4	no	—
160	C₂×C₇×D₄	—	2	4	no	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	—	2	8	no	—
163	C₂×C₇×D₄	—	2	8	no	—
164	C₂×C₇×D₄	—	4	4	no	—
165	C₂×C₇×D₄	—	4	8	no	—
166	C₂×C₇×D₄	—	8	4	no	—
167	C₂×C₇×D₄	—	8	4	no	—
168	C₂×C₇×D₄	C₂×D₄	1	8	yes	—
169	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
170	C₂×C₇×D₄	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₇	—	2	4	no	—
172	C₂²×C₄×C₇	—	2	4	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	1	no	—
175	C₂²×C₄×C₇	—	2	1	no	—
176	C₂²×C₄×C₇	—	2	1	no	—
177	C₂²×C₄×C₇	—	2	2	no	—
178	C₂²×C₄×C₇	—	2	4	no	—
179	C₂²×C₄×C₇	—	2	8	no	—
180	C₂²×C₄×C₇	—	8	2	no	—
181	C₂²×C₄×C₇	—	8	4	no	—
182	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
183	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₇	#41	1	4	yes	—
187	C₂²×C₄×C₇	#41	1	4	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
191	C₇×M₁₆	—	2	8	no	—
192	C₂×C₇×C₈	—	2	2	no	—
193	C₂×C₇×C₈	—	2	2	no	—
194	C₂×C₇×C₈	—	2	8	no	—
195	C₂×C₇×C₈	—	2	4	no	—
196	C₂×C₇×C₈	C₂⁴	1	2	yes	—
197	C₂×C₇×C₈	C₂⁴	1	4	yes	—
198	C₂×C₇×C₈	C₂⁴	1	2	yes	—
199	C₇×C₄⋊C₄	—	2	2	no	—
200	C₇×C₄⋊C₄	—	2	1	no	—
201	C₇×C₄⋊C₄	—	2	4	no	—
202	C₇×C₄⋊C₄	—	2	8	no	—
203	C₇×C₄⋊C₄	—	2	1	no	—
204	C₇×C₄⋊C₄	—	2	1	no	—
205	C₇×C₄⋊C₄	—	2	1	no	—
206	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
207	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
208	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
209	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
210	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
211	C₇×C₂²⋊C₄	—	2	4	no	—
212	C₇×C₂²⋊C₄	—	2	4	no	—
213	C₇×C₂²⋊C₄	—	2	8	no	—
214	C₇×C₂²⋊C₄	—	2	8	no	—
215	C₇×C₂²⋊C₄	—	2	8	no	—
216	C₄²×C₇	—	2	4	no	—
217	C₄²×C₇	—	2	4	no	—
218	C₄²×C₇	—	2	8	no	—
219	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
220	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
222	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
223	#535	—	2	4	no	—
224	#535	C₂²×C₇	1	8	yes	—
225	C₂×#127	—	2	1	no	—
226	C₂×#124	—	2	1	no	—
227	C₂×#121	C₂²×C₇	1	2	yes	—
228	C₂×#121	C₂²×C₇	1	2	yes	—
229	C₂×#120	—	2	2	no	—
230	#520	—	2	4	no	—
231	#520	C₂²×C₇	1	8	yes	complemented
232	C₂×C₄×Q₈	—	2	1	no	—
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	—	2	2	no	—
235	C₂×#117	C₂²×C₇	1	1	yes	characteristic
236	C₂×#117	C₂²×C₇	1	1	yes	characteristic
237	C₂×#117	C₂²×C₇	1	2	yes	complemented
238	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
240	#482	C₂²×C₇	1	16	yes	complemented
241	#482	C₂²×C₇	1	16	yes	complemented
242	#481	C₂²×C₇	1	16	yes	complemented
243	#480	C₂²×C₇	1	16	yes	complemented
244	#428	C₂²×C₇	1	8	yes	complemented
245	#427	C₂²×C₇	1	8	yes	complemented
246	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
247	C₂×#107	C₂²×C₇	1	2	yes	complemented
248	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
249	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
250	C₂×#106	C₂²×C₇	1	2	yes	complemented
251	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
252	#418	C₂²×C₇	1	8	yes	complemented
253	C₂×#102	C₂²×C₇	1	2	yes	—
254	C₂×#102	C₂²×C₇	1	2	yes	—
255	C₂×#102	C₂²×C₇	1	2	yes	—
256	C₂×#102	C₂²×C₇	1	2	yes	—
257	C₂×#102	C₂²×C₇	1	8	yes	complemented
258	#408	C₂²×C₇	1	8	yes	complemented
259	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
260	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
261	C₂³×C₇	—	2	2	no	—
262	C₂³×C₇	—	2	2	no	—
263	C₂³×C₇	—	2	4	no	—
264	C₂³×C₇	—	2	4	no	—
265	C₂³×C₇	—	2	4	no	—
266	C₂³×C₇	—	2	4	no	—
267	C₂³×C₇	—	4	8	no	—
268	C₂³×C₇	—	4	4	no	—
269	C₂³×C₇	—	4	4	no	—
270	C₂³×C₇	—	4	4	no	—
271	C₂³×C₇	—	8	4	no	—
272	C₂³×C₇	—	8	4	no	—
273	C₂³×C₇	—	8	16	no	—
274	C₂³×C₇	#123	1	4	yes	—
275	C₂³×C₇	C₂²×D₄	1	4	yes	—
276	C₂³×C₇	C₂²×D₄	1	2	yes	—
277	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
278	C₇×Q₈	—	2	8	no	—
279	C₇×D₄	—	2	16	no	—
280	C₇×D₄	—	2	8	no	—
281	C₇×D₄	—	2	4	no	—
282	C₇×D₄	—	2	4	no	—
283	C₇×D₄	—	4	4	no	—
284	C₇×D₄	—	4	8	no	—
285	C₇×D₄	—	8	8	no	—
286	C₇×D₄	—	8	8	no	—
287	C₂×C₄×C₇	—	2	4	no	—
288	C₂×C₄×C₇	—	2	8	no	—
289	C₂×C₄×C₇	—	2	4	no	—
290	C₂×C₄×C₇	—	2	4	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	2	no	—
293	C₂×C₄×C₇	—	2	2	no	—
294	C₂×C₄×C₇	—	2	2	no	—
295	C₂×C₄×C₇	—	2	4	no	—
296	C₂×C₄×C₇	—	4	2	no	—
297	C₂×C₄×C₇	—	4	4	no	—
298	C₂×C₄×C₇	—	4	2	no	—
299	C₂×C₄×C₇	—	4	2	no	—
300	C₂×C₄×C₇	—	4	2	no	—
301	C₂×C₄×C₇	—	8	4	no	—
302	C₂×C₄×C₇	—	8	8	no	—
303	C₂×C₄×C₇	#123	1	4	yes	—
304	C₂×C₄×C₇	#123	1	8	yes	—
305	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
306	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₇	C₂×#41	1	2	yes	—
309	C₂×C₄×C₇	C₂×#41	1	2	yes	—
310	C₂×C₄×C₇	C₂×#41	1	4	yes	—
311	C₂×C₄×C₇	C₂×#41	1	4	yes	—
312	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
313	C₇×C₈	—	2	2	no	—
314	C₇×C₈	—	2	2	no	—
315	C₇×C₈	—	2	4	no	—
316	C₂⁵	—	2	1	no	—
317	C₂×#41	—	2	4	no	—
318	C₂×#41	—	2	4	no	—
319	C₂×#41	C₇×D₄	1	4	yes	—
320	C₂×#41	C₂³×C₇	1	4	yes	—
321	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	2	no	—
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	C₇×D₄	1	2	yes	—
329	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
330	C₂²×D₄	C₂³×C₇	1	2	yes	—
331	C₂²×D₄	C₂³×C₇	1	4	yes	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	2	no	—
334	C₂³×C₄	C₂³×C₇	1	2	yes	—
335	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
336	C₂×M₁₆	—	2	4	no	—
337	C₂×M₁₆	C₂³×C₇	1	4	yes	—
338	C₂²×C₈	—	2	4	no	—
339	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₇	1	4	yes	—
342	C₂²×C₈	C₂³×C₇	1	2	yes	—
343	#127	—	2	8	no	—
344	#124	—	2	8	no	—
345	#121	—	2	4	no	—
346	#121	—	2	4	no	—
347	#121	C₂³×C₇	1	8	yes	—
348	#121	C₂³×C₇	1	8	yes	—
349	#120	—	2	16	no	—
350	C₄×Q₈	—	2	8	no	—
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	2	16	no	—
353	#117	—	2	2	no	—
354	#117	—	2	2	no	—
355	#117	—	2	4	no	—
356	#117	C₂³×C₇	1	4	yes	—
357	#117	C₂³×C₇	1	4	yes	—
358	#117	C₂³×C₇	1	8	yes	complemented
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	4	no	—
363	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	2	no	—
378	#107	C₂³×C₇	1	4	yes	complemented
379	#107	C₂³×C₇	1	4	yes	complemented
380	#107	C₂³×C₇	1	8	yes	complemented
381	#106	C₂³×C₇	1	4	yes	complemented
382	#106	C₂³×C₇	1	4	yes	complemented
383	#106	C₂³×C₇	1	8	yes	complemented
384	#102	C₂³×C₇	1	8	yes	—
385	#102	C₂³×C₇	1	8	yes	—
386	#102	C₂³×C₇	1	8	yes	—
387	#102	C₂³×C₇	1	8	yes	—
388	C₂²⋊C₈	C₂³×C₇	1	8	yes	complemented
389	C₂²⋊C₈	C₂³×C₇	1	8	yes	complemented
390	C₂²×C₇	—	2	8	no	—
391	C₂²×C₇	—	2	2	no	—
392	C₂²×C₇	—	2	2	no	—
393	C₂²×C₇	—	2	4	no	—
394	C₂²×C₇	—	2	4	no	—
395	C₂²×C₇	—	2	4	no	—
396	C₂²×C₇	—	4	8	no	—
397	C₂²×C₇	—	4	4	no	—
398	C₂²×C₇	—	4	4	no	—
399	C₂²×C₇	—	4	4	no	—
400	C₂²×C₇	—	8	16	no	—
401	C₂²×C₇	—	8	8	no	—
402	C₂²×C₇	C₂×#123	1	4	yes	—
403	C₂²×C₇	C₂×#123	1	2	yes	—
404	C₂²×C₇	#576	1	2	yes	—
405	C₂²×C₇	#577	1	2	yes	—
406	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₇	—	2	4	no	—
408	C₄×C₇	—	4	2	no	—
409	C₄×C₇	—	4	4	no	—
410	C₄×C₇	—	4	2	no	—
411	C₄×C₇	—	4	2	no	—
412	C₄×C₇	—	4	2	no	—
413	C₄×C₇	C₂×#123	1	2	yes	—
414	C₄×C₇	C₂×#123	1	4	yes	—
415	C₄×C₇	C₂²×#41	1	1	yes	characteristic
416	C₄×C₇	C₂²×#41	1	1	yes	characteristic
417	C₂⁴	—	2	2	no	—
418	C₂⁴	—	2	4	no	—
419	C₂⁴	—	4	4	no	—
420	C₂⁴	—	8	2	no	—
421	C₂⁴	—	8	2	no	—
422	C₂⁴	C₂×C₇×D₄	1	2	yes	—
423	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
424	#41	—	2	16	no	—
425	#41	—	2	8	no	—
426	#41	—	2	8	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	8	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	8	no	—
441	C₂×D₄	—	8	4	no	—
442	C₂×D₄	—	8	4	no	—
443	C₂×D₄	C₂×C₇×D₄	1	8	yes	—
444	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
445	C₂×D₄	C₂⁴×C₇	1	4	yes	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	8	no	—
455	C₂²×C₄	—	8	2	no	—
456	C₂²×C₄	—	8	4	no	—
457	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
458	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
459	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
461	C₂²×C₄	C₇×#41	1	4	yes	—
462	C₂²×C₄	C₇×#41	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
466	M₁₆	—	2	8	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	8	no	—
470	C₂×C₈	—	2	4	no	—
471	C₂×C₈	C₂⁴×C₇	1	2	yes	—
472	C₂×C₈	C₂⁴×C₇	1	4	yes	—
473	C₂×C₈	C₂⁴×C₇	1	2	yes	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
482	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
483	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
484	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
485	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	8	no	—
494	C₂×C₇	—	2	4	no	—
495	C₂×C₇	—	4	4	no	—
496	C₂×C₇	—	8	4	no	—
497	C₂×C₇	#3096	1	4	yes	direct product factor
498	C₂×C₇	C₂²×#123	1	1	yes	characteristic
499	C₂×C₇	C₂×#576	1	1	yes	characteristic
500	C₂×C₇	C₂×#577	1	1	yes	characteristic
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	8	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	4	no	—
510	C₂³	—	4	4	no	—
511	C₂³	—	8	4	no	—
512	C₂³	—	8	4	no	—
513	C₂³	—	8	16	no	—
514	C₂³	C₇×#123	1	4	yes	—
515	C₂³	C₂²×C₇×D₄	1	4	yes	—
516	C₂³	C₂²×C₇×D₄	1	2	yes	—
517	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
518	Q₈	—	2	8	no	—
519	D₄	—	2	16	no	—
520	D₄	—	2	4	no	—
521	D₄	—	2	4	no	—
522	D₄	—	2	8	no	—
523	D₄	—	4	4	no	—
524	D₄	—	4	8	no	—
525	D₄	—	8	8	no	—
526	D₄	—	8	8	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	4	no	—
542	C₂×C₄	—	8	8	no	—
543	C₂×C₄	C₇×#123	1	4	yes	—
544	C₂×C₄	C₇×#123	1	8	yes	—
545	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
546	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
547	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
548	C₂×C₄	C₂×C₇×#41	1	2	yes	—
549	C₂×C₄	C₂×C₇×#41	1	2	yes	—
550	C₂×C₄	C₂×C₇×#41	1	4	yes	—
551	C₂×C₄	C₂×C₇×#41	1	4	yes	—
552	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
553	C₈	—	2	2	no	—
554	C₈	—	2	2	no	—
555	C₈	—	2	4	no	—
556	C₇	C₂×#3096	1	1	yes	characteristic, direct product factor, Sylow
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	8	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	4	8	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	8	16	no	—
568	C₂²	—	8	8	no	—
569	C₂²	C₂×C₇×#123	1	4	yes	—
570	C₂²	C₂×C₇×#123	1	2	yes	—
571	C₂²	C₇×#576	1	2	yes	—
572	C₂²	C₇×#577	1	2	yes	—
573	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
574	C₄	—	2	4	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	4	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	2	no	—
580	C₄	C₂×C₇×#123	1	2	yes	—
581	C₄	C₂×C₇×#123	1	4	yes	—
582	C₄	C₂²×C₇×#41	1	1	yes	characteristic
583	C₄	C₂²×C₇×#41	1	1	yes	characteristic
584	C₂	—	2	4	no	—
585	C₂	—	4	4	no	—
586	C₂	—	8	4	no	—
587	C₂	C₇×#3096	1	4	yes	direct product factor
588	C₂	C₂²×C₇×#123	1	1	yes	characteristic
589	C₂	C₂×C₇×#576	1	1	yes	characteristic
590	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	C₂×C₇×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#520	C₂	semidirect
3. C₇×#3096	C₂	direct (N × H)
4. C₂×C₇×#481	C₂	semidirect
5. C₂×C₇×#482	C₂	semidirect
6. C₂×C₇×#482	C₂	semidirect
7. C₂×C₇×#480	C₂	semidirect
8. C₂×C₇×#428	C₂	semidirect
9. C₂×C₇×#427	C₂	semidirect
10. C₂×C₇×#418	C₂	semidirect
11. C₂²×C₇×#102	C₂	semidirect
12. C₂×C₇×#408	C₂	semidirect
25. C₇×#520	C₂²	semidirect
31. C₂×C₇×#117	C₂²	semidirect
33. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
34. C₇×#482	C₂²	semidirect
35. C₇×#482	C₂²	semidirect
36. C₇×#481	C₂²	semidirect
37. C₇×#480	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×#418	C₂²	semidirect
51. C₂×C₇×#102	C₂²	semidirect
52. C₇×#408	C₂²	semidirect
53. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
54. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
55. C₂×#3096	C₇	direct (N × H)
98. C₇×#117	C₂³	semidirect
109. C₂×C₇×C₄⋊C₄	C₂³	semidirect
118. C₇×#107	C₂³	semidirect
119. C₇×#107	C₂³	semidirect
120. C₇×#107	C₂³	semidirect
121. C₇×#106	C₂³	semidirect
122. C₇×#106	C₂³	semidirect
123. C₇×#106	C₂³	semidirect
128. C₇×C₂²⋊C₈	C₂³	semidirect
129. C₇×C₂²⋊C₈	C₂³	semidirect
131. C₂×#520	C₂×C₇	semidirect
132. #3096	C₂×C₇	direct (N × H)
133. C₂×#481	C₂×C₇	semidirect
134. C₂×#482	C₂×C₇	semidirect
135. C₂×#482	C₂×C₇	semidirect
136. C₂×#480	C₂×C₇	semidirect
137. C₂×#428	C₂×C₇	semidirect
138. C₂×#427	C₂×C₇	semidirect
139. C₂×#418	C₂×C₇	semidirect
140. C₂²×#102	C₂×C₇	semidirect
141. C₂×#408	C₂×C₇	semidirect
231. #520	C₂²×C₇	semidirect
237. C₂×#117	C₂²×C₇	semidirect
239. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
240. #482	C₂²×C₇	semidirect
241. #482	C₂²×C₇	semidirect
242. #481	C₂²×C₇	semidirect
243. #480	C₂²×C₇	semidirect
244. #428	C₂²×C₇	semidirect
245. #427	C₂²×C₇	semidirect
246. C₂×#107	C₂²×C₇	semidirect
247. C₂×#107	C₂²×C₇	semidirect
248. C₂×#107	C₂²×C₇	semidirect
249. C₂×#106	C₂²×C₇	semidirect
250. C₂×#106	C₂²×C₇	semidirect
251. C₂×#106	C₂²×C₇	semidirect
252. #418	C₂²×C₇	semidirect
257. C₂×#102	C₂²×C₇	semidirect
258. #408	C₂²×C₇	semidirect
259. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
260. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
358. #117	C₂³×C₇	semidirect
369. C₂×C₄⋊C₄	C₂³×C₇	semidirect
378. #107	C₂³×C₇	semidirect
379. #107	C₂³×C₇	semidirect
380. #107	C₂³×C₇	semidirect
381. #106	C₂³×C₇	semidirect
382. #106	C₂³×C₇	semidirect
383. #106	C₂³×C₇	semidirect
388. C₂²⋊C₈	C₂³×C₇	semidirect
389. C₂²⋊C₈	C₂³×C₇	semidirect
497. C₂×C₇	#3096	direct (N × H)
556. C₇	C₂×#3096	direct (N × H)
587. C₂	C₇×#3096	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×#535	2
C₂×C₇×#520	2
C₇×#3096	2
C₂×C₇×#481	2
C₂×C₇×#482	2
C₂×C₇×#480	2
C₂×C₇×#428	2
C₂×C₇×#427	2
C₂×C₇×#418	2
C₂²×C₇×#102	2
C₂×C₇×#408	2
C₂×#3096	7

Subgroups — C2×C7×#3096 #13237728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3096 #13237728