Subgroups — C₂×C₇×#3091 #13237722

Order 1792.

2378 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#525	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3091	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#480	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#427	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#416	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	2	yes	—
16	C₇×#525	—	2	4	no	—
17	C₇×#525	C₂²	1	8	yes	—
18	C₂×C₇×#123	—	2	1	no	—
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#121	C₂²	1	1	yes	characteristic
22	C₂×C₇×#121	C₂²	1	1	yes	characteristic
23	C₂×C₇×#120	—	2	1	no	—
24	C₂×C₄×C₇×D₄	—	2	1	no	—
25	C₂×C₄×C₇×D₄	—	2	1	no	—
26	C₂×C₇×#117	—	2	1	no	—
27	C₂×C₇×#117	—	2	4	no	—
28	C₂×C₇×#117	—	2	1	no	—
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	C₂²	1	2	yes	—
31	C₂×C₇×#117	C₂²	1	2	yes	—
32	C₂×C₇×#117	C₂²	1	8	yes	complemented
33	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
36	C₂²×C₄²×C₇	—	2	1	no	—
37	C₇×#485	C₂²	1	16	yes	complemented
38	C₇×#484	C₂²	1	8	yes	complemented
39	C₇×#483	C₂²	1	8	yes	complemented
40	C₇×#482	C₂²	1	16	yes	complemented
41	C₇×#481	C₂²	1	8	yes	complemented
42	C₇×#480	C₂²	1	8	yes	complemented
43	C₇×#427	C₂²	1	16	yes	complemented
44	C₂×C₇×#107	C₂²	1	2	yes	complemented
45	C₂×C₇×#107	C₂²	1	2	yes	complemented
46	C₂×C₇×#106	C₂²	1	2	yes	complemented
47	C₂×C₇×#106	C₂²	1	2	yes	complemented
48	C₇×#416	C₂²	1	16	yes	complemented
49	C₂×C₇×#103	C₂²	1	2	yes	complemented
50	C₂×C₇×#103	C₂²	1	2	yes	complemented
51	C₂×C₇×#102	C₂²	1	2	yes	complemented
52	C₂×C₇×#102	C₂²	1	2	yes	complemented
53	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
56	C₂×C₇×C₂²⋊C₈	C₂²	1	8	yes	complemented
57	C₂×#3091	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂⁵×C₇	D₄	1	1	yes	characteristic
59	C₂×C₇×#41	—	2	2	no	—
60	C₂×C₇×#41	—	2	8	no	—
61	C₂×C₇×#41	C₂³	1	4	yes	—
62	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×D₄	—	2	1	no	—
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	—	2	1	no	—
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	8	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂³×C₄×C₇	—	2	1	no	—
71	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₇	D₄	1	4	yes	—
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	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₇	C₂³	1	4	yes	—
78	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₂²×C₇×C₈	—	2	8	no	—
80	C₂²×C₇×C₈	C₂³	1	2	yes	—
81	C₂²×C₇×C₈	C₂³	1	2	yes	—
82	C₂²×C₇×C₈	C₂³	1	8	yes	—
83	C₇×#123	—	2	8	no	—
84	C₇×C₂²⋊Q₈	—	2	2	no	—
85	C₇×C₂²⋊Q₈	—	2	2	no	—
86	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
87	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
88	C₇×#121	—	2	2	no	—
89	C₇×#121	—	2	2	no	—
90	C₇×#121	C₂³	1	4	yes	—
91	C₇×#121	C₂³	1	4	yes	—
92	C₇×#120	—	2	8	no	—
93	C₄×C₇×D₄	—	2	8	no	—
94	C₄×C₇×D₄	—	2	8	no	—
95	C₇×#117	—	2	4	no	—
96	C₇×#117	—	2	4	no	—
97	C₇×#117	—	2	8	no	—
98	C₇×#117	—	2	8	no	—
99	C₇×#117	—	2	2	no	—
100	C₇×#117	C₂³	1	8	yes	—
101	C₇×#117	C₂³	1	8	yes	—
102	C₇×#117	C₂³	1	4	yes	—
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	—	2	2	no	—
106	C₂×C₇×C₄⋊C₄	—	2	2	no	—
107	C₂×C₇×C₄⋊C₄	—	2	1	no	—
108	C₂×C₇×C₄⋊C₄	—	2	1	no	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
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	2	yes	—
113	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₇×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₄²×C₇	—	2	2	no	—
124	C₂×C₄²×C₇	—	2	8	no	—
125	C₂×C₄²×C₇	—	2	2	no	—
126	C₂×C₄²×C₇	—	2	1	no	—
127	C₇×#107	C₂³	1	8	yes	complemented
128	C₇×#107	C₂³	1	8	yes	complemented
129	C₇×#106	C₂³	1	8	yes	complemented
130	C₇×#106	C₂³	1	8	yes	complemented
131	C₇×#103	C₂³	1	8	yes	complemented
132	C₇×#103	C₂³	1	8	yes	complemented
133	C₇×#102	C₂³	1	8	yes	complemented
134	C₇×#102	C₂³	1	8	yes	complemented
135	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
136	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
137	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
138	C₂×#525	C₂×C₇	1	1	yes	characteristic
139	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
140	#3091	C₂×C₇	1	16	yes	direct product factor
141	C₂×#484	C₂×C₇	1	1	yes	characteristic, complemented
142	C₂×#481	C₂×C₇	1	1	yes	characteristic, complemented
143	C₂×#485	C₂×C₇	1	2	yes	complemented
144	C₂×#482	C₂×C₇	1	2	yes	complemented
145	C₂×#483	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂×#480	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#427	C₂×C₇	1	2	yes	complemented
148	C₂×#416	C₂×C₇	1	2	yes	complemented
149	C₂²×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
150	C₂⁴×C₇	—	2	4	no	—
151	C₂⁴×C₇	—	2	4	no	—
152	C₂⁴×C₇	—	2	1	no	—
153	C₂⁴×C₇	—	4	2	no	—
154	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
155	C₂⁴×C₇	C₂×D₄	1	4	yes	—
156	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
158	C₇×#41	—	2	16	no	—
159	C₇×#41	—	4	8	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	4	no	—
162	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
163	C₂×C₇×D₄	—	2	4	no	—
164	C₂×C₇×D₄	—	2	4	no	—
165	C₂×C₇×D₄	—	2	4	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	2	4	no	—
168	C₂×C₇×D₄	—	4	4	no	—
169	C₂×C₇×D₄	—	4	4	no	—
170	C₂×C₇×D₄	—	4	4	no	—
171	C₂×C₇×D₄	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₇	—	2	4	no	—
173	C₂²×C₄×C₇	—	2	4	no	—
174	C₂²×C₄×C₇	—	2	4	no	—
175	C₂²×C₄×C₇	—	2	16	no	—
176	C₂²×C₄×C₇	—	2	4	no	—
177	C₂²×C₄×C₇	—	2	4	no	—
178	C₂²×C₄×C₇	—	2	16	no	—
179	C₂²×C₄×C₇	—	2	4	no	—
180	C₂²×C₄×C₇	—	2	4	no	—
181	C₂²×C₄×C₇	—	2	2	no	—
182	C₂²×C₄×C₇	—	2	2	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	4	no	—
187	C₂²×C₄×C₇	—	4	4	no	—
188	C₂²×C₄×C₇	—	4	4	no	—
189	C₂²×C₄×C₇	—	4	4	no	—
190	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
194	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
195	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
197	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	#41	1	8	yes	—
200	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
204	C₂×C₇×C₈	—	2	4	no	—
205	C₂×C₇×C₈	—	2	4	no	—
206	C₂×C₇×C₈	—	2	16	no	—
207	C₂×C₇×C₈	C₂⁴	1	4	yes	—
208	C₂×C₇×C₈	C₂⁴	1	4	yes	—
209	C₇×C₄⋊C₄	—	2	4	no	—
210	C₇×C₄⋊C₄	—	2	4	no	—
211	C₇×C₄⋊C₄	—	2	2	no	—
212	C₇×C₄⋊C₄	—	2	2	no	—
213	C₇×C₄⋊C₄	—	2	4	no	—
214	C₇×C₄⋊C₄	—	2	4	no	—
215	C₇×C₄⋊C₄	—	2	1	no	—
216	C₇×C₄⋊C₄	—	2	1	no	—
217	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
218	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
219	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
220	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
221	C₇×C₂²⋊C₄	—	2	8	no	—
222	C₇×C₂²⋊C₄	—	2	8	no	—
223	C₇×C₂²⋊C₄	—	2	4	no	—
224	C₇×C₂²⋊C₄	—	2	4	no	—
225	C₇×C₂²⋊C₄	—	2	4	no	—
226	C₇×C₂²⋊C₄	—	2	4	no	—
227	C₇×C₂²⋊C₄	—	2	4	no	—
228	C₄²×C₇	—	2	8	no	—
229	C₄²×C₇	—	2	8	no	—
230	C₄²×C₇	—	2	4	no	—
231	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
232	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
233	C₂³×C₈	C₂²×C₇	1	2	yes	—
234	#525	—	2	4	no	—
235	#525	C₂²×C₇	1	8	yes	—
236	C₂×#123	—	2	1	no	—
237	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
238	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
239	C₂×#121	C₂²×C₇	1	1	yes	characteristic
240	C₂×#121	C₂²×C₇	1	1	yes	characteristic
241	C₂×#120	—	2	1	no	—
242	C₂×C₄×D₄	—	2	1	no	—
243	C₂×C₄×D₄	—	2	1	no	—
244	C₂×#117	—	2	1	no	—
245	C₂×#117	—	2	1	no	—
246	C₂×#117	—	2	4	no	—
247	C₂×#117	C₂²×C₇	1	2	yes	—
248	C₂×#117	C₂²×C₇	1	2	yes	—
249	C₂×#117	C₂²×C₇	1	1	yes	characteristic
250	C₂×#117	C₂²×C₇	1	8	yes	complemented
251	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	—	2	1	no	—
254	C₂²×C₄²	—	2	1	no	—
255	#485	C₂²×C₇	1	16	yes	complemented
256	#484	C₂²×C₇	1	8	yes	complemented
257	#483	C₂²×C₇	1	8	yes	complemented
258	#482	C₂²×C₇	1	16	yes	complemented
259	#481	C₂²×C₇	1	8	yes	complemented
260	#480	C₂²×C₇	1	8	yes	complemented
261	#427	C₂²×C₇	1	16	yes	complemented
262	C₂×#107	C₂²×C₇	1	2	yes	complemented
263	C₂×#107	C₂²×C₇	1	2	yes	complemented
264	C₂×#106	C₂²×C₇	1	2	yes	complemented
265	C₂×#106	C₂²×C₇	1	2	yes	complemented
266	#416	C₂²×C₇	1	16	yes	complemented
267	C₂×#103	C₂²×C₇	1	2	yes	complemented
268	C₂×#103	C₂²×C₇	1	2	yes	complemented
269	C₂×#102	C₂²×C₇	1	2	yes	complemented
270	C₂×#102	C₂²×C₇	1	2	yes	complemented
271	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₇	1	8	yes	complemented
275	C₂³×C₇	—	2	2	no	—
276	C₂³×C₇	—	2	2	no	—
277	C₂³×C₇	—	2	2	no	—
278	C₂³×C₇	—	2	2	no	—
279	C₂³×C₇	—	2	8	no	—
280	C₂³×C₇	—	2	2	no	—
281	C₂³×C₇	—	2	8	no	—
282	C₂³×C₇	—	2	2	no	—
283	C₂³×C₇	—	2	2	no	—
284	C₂³×C₇	—	2	2	no	—
285	C₂³×C₇	—	4	4	no	—
286	C₂³×C₇	—	4	16	no	—
287	C₂³×C₇	—	4	2	no	—
288	C₂³×C₇	—	4	2	no	—
289	C₂³×C₇	—	4	2	no	—
290	C₂³×C₇	#123	1	4	yes	—
291	C₂³×C₇	#135	1	4	yes	—
292	C₂³×C₇	C₂²×D₄	1	2	yes	—
293	C₂³×C₇	C₂²×D₄	1	2	yes	—
294	C₂³×C₇	C₂²×D₄	1	2	yes	—
295	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
296	C₇×Q₈	—	2	4	no	—
297	C₇×Q₈	—	4	2	no	—
298	C₇×D₄	—	2	4	no	—
299	C₇×D₄	—	4	8	no	—
300	C₇×D₄	—	4	8	no	—
301	C₇×D₄	—	4	8	no	—
302	C₇×D₄	—	4	2	no	—
303	C₂×C₄×C₇	—	2	8	no	—
304	C₂×C₄×C₇	—	2	2	no	—
305	C₂×C₄×C₇	—	2	2	no	—
306	C₂×C₄×C₇	—	2	8	no	—
307	C₂×C₄×C₇	—	2	8	no	—
308	C₂×C₄×C₇	—	2	4	no	—
309	C₂×C₄×C₇	—	2	4	no	—
310	C₂×C₄×C₇	—	2	4	no	—
311	C₂×C₄×C₇	—	2	4	no	—
312	C₂×C₄×C₇	—	2	4	no	—
313	C₂×C₄×C₇	—	2	4	no	—
314	C₂×C₄×C₇	—	2	2	no	—
315	C₂×C₄×C₇	—	2	2	no	—
316	C₂×C₄×C₇	—	2	2	no	—
317	C₂×C₄×C₇	—	4	8	no	—
318	C₂×C₄×C₇	—	4	2	no	—
319	C₂×C₄×C₇	—	4	8	no	—
320	C₂×C₄×C₇	—	4	4	no	—
321	C₂×C₄×C₇	—	4	2	no	—
322	C₂×C₄×C₇	—	4	4	no	—
323	C₂×C₄×C₇	—	4	2	no	—
324	C₂×C₄×C₇	—	4	8	no	—
325	C₂×C₄×C₇	#123	1	4	yes	—
326	C₂×C₄×C₇	#123	1	8	yes	—
327	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₇	C₂×#41	1	4	yes	—
332	C₂×C₄×C₇	C₂×#41	1	8	yes	—
333	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
334	C₇×C₈	—	2	4	no	—
335	C₇×C₈	—	2	4	no	—
336	C₂⁵	C₇×D₄	1	1	yes	characteristic
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	8	no	—
339	C₂×#41	C₂³×C₇	1	4	yes	—
340	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
345	C₂³×C₄	—	2	8	no	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
350	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
351	C₂³×C₄	C₇×D₄	1	4	yes	—
352	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₇	1	4	yes	—
356	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂²×C₈	—	2	8	no	—
358	C₂²×C₈	C₂³×C₇	1	2	yes	—
359	C₂²×C₈	C₂³×C₇	1	2	yes	—
360	C₂²×C₈	C₂³×C₇	1	8	yes	—
361	#123	—	2	8	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
365	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
366	#121	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	C₂³×C₇	1	4	yes	—
369	#121	C₂³×C₇	1	4	yes	—
370	#120	—	2	8	no	—
371	C₄×D₄	—	2	8	no	—
372	C₄×D₄	—	2	8	no	—
373	#117	—	2	4	no	—
374	#117	—	2	4	no	—
375	#117	—	2	8	no	—
376	#117	—	2	8	no	—
377	#117	—	2	2	no	—
378	#117	C₂³×C₇	1	8	yes	—
379	#117	C₂³×C₇	1	8	yes	—
380	#117	C₂³×C₇	1	4	yes	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	2	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	—	2	8	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₄²	—	2	2	no	—
402	C₂×C₄²	—	2	2	no	—
403	C₂×C₄²	—	2	8	no	—
404	C₂×C₄²	—	2	1	no	—
405	#107	C₂³×C₇	1	8	yes	complemented
406	#107	C₂³×C₇	1	8	yes	complemented
407	#106	C₂³×C₇	1	8	yes	complemented
408	#106	C₂³×C₇	1	8	yes	complemented
409	#103	C₂³×C₇	1	8	yes	complemented
410	#103	C₂³×C₇	1	8	yes	complemented
411	#102	C₂³×C₇	1	8	yes	complemented
412	#102	C₂³×C₇	1	8	yes	complemented
413	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
414	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
415	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
416	C₂²×C₇	—	2	8	no	—
417	C₂²×C₇	—	2	8	no	—
418	C₂²×C₇	—	2	2	no	—
419	C₂²×C₇	—	2	2	no	—
420	C₂²×C₇	—	2	2	no	—
421	C₂²×C₇	—	2	2	no	—
422	C₂²×C₇	—	2	2	no	—
423	C₂²×C₇	—	2	2	no	—
424	C₂²×C₇	—	2	2	no	—
425	C₂²×C₇	—	4	16	no	—
426	C₂²×C₇	—	4	4	no	—
427	C₂²×C₇	—	4	2	no	—
428	C₂²×C₇	—	4	2	no	—
429	C₂²×C₇	—	4	2	no	—
430	C₂²×C₇	—	8	4	no	—
431	C₂²×C₇	C₂×#123	1	4	yes	—
432	C₂²×C₇	C₂×#123	1	2	yes	—
433	C₂²×C₇	C₂×#135	1	4	yes	—
434	C₂²×C₇	C₂×#135	1	2	yes	—
435	C₂²×C₇	#575	1	2	yes	—
436	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₇	—	2	2	no	—
438	C₄×C₇	—	2	2	no	—
439	C₄×C₇	—	4	2	no	—
440	C₄×C₇	—	4	4	no	—
441	C₄×C₇	—	4	2	no	—
442	C₄×C₇	—	4	4	no	—
443	C₄×C₇	—	4	2	no	—
444	C₄×C₇	C₂×#123	1	4	yes	—
445	C₄×C₇	C₂×#123	1	2	yes	—
446	C₄×C₇	C₂²×#41	1	2	yes	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	2	1	no	—
450	C₂⁴	—	4	2	no	—
451	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
452	C₂⁴	C₂×C₇×D₄	1	4	yes	—
453	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
454	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
455	#41	—	2	16	no	—
456	#41	—	4	8	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	4	no	—
459	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	C₂⁴×C₇	1	2	yes	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	16	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	16	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	4	4	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	4	4	no	—
487	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
489	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
491	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
492	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
493	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
494	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
495	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
496	C₂²×C₄	C₇×#41	1	8	yes	—
497	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
501	C₂×C₈	—	2	4	no	—
502	C₂×C₈	—	2	4	no	—
503	C₂×C₈	—	2	16	no	—
504	C₂×C₈	C₂⁴×C₇	1	4	yes	—
505	C₂×C₈	C₂⁴×C₇	1	4	yes	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
515	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
516	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
517	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₄²	—	2	8	no	—
526	C₄²	—	2	8	no	—
527	C₄²	—	2	4	no	—
528	C₂×C₇	—	2	4	no	—
529	C₂×C₇	—	2	4	no	—
530	C₂×C₇	—	4	2	no	—
531	C₂×C₇	—	8	2	no	—
532	C₂×C₇	#3091	1	4	yes	direct product factor
533	C₂×C₇	C₂²×#123	1	1	yes	characteristic
534	C₂×C₇	C₂²×#135	1	1	yes	characteristic
535	C₂×C₇	C₂×#575	1	1	yes	characteristic
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	8	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	16	no	—
548	C₂³	—	4	2	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	C₇×#123	1	4	yes	—
552	C₂³	C₇×#135	1	4	yes	—
553	C₂³	C₂²×C₇×D₄	1	2	yes	—
554	C₂³	C₂²×C₇×D₄	1	2	yes	—
555	C₂³	C₂²×C₇×D₄	1	2	yes	—
556	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
557	Q₈	—	2	4	no	—
558	Q₈	—	4	2	no	—
559	D₄	—	2	4	no	—
560	D₄	—	4	8	no	—
561	D₄	—	4	8	no	—
562	D₄	—	4	8	no	—
563	D₄	—	4	2	no	—
564	C₂×C₄	—	2	8	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	8	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	4	8	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	8	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	8	no	—
586	C₂×C₄	C₇×#123	1	4	yes	—
587	C₂×C₄	C₇×#123	1	8	yes	—
588	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
589	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
590	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
591	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
592	C₂×C₄	C₂×C₇×#41	1	4	yes	—
593	C₂×C₄	C₂×C₇×#41	1	8	yes	—
594	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
595	C₈	—	2	4	no	—
596	C₈	—	2	4	no	—
597	C₇	C₂×#3091	1	1	yes	characteristic, direct product factor, Sylow
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	8	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	16	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	8	4	no	—
613	C₂²	C₂×C₇×#123	1	4	yes	—
614	C₂²	C₂×C₇×#123	1	2	yes	—
615	C₂²	C₂×C₇×#135	1	4	yes	—
616	C₂²	C₂×C₇×#135	1	2	yes	—
617	C₂²	C₇×#575	1	2	yes	—
618	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	4	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	C₂×C₇×#123	1	4	yes	—
627	C₄	C₂×C₇×#123	1	2	yes	—
628	C₄	C₂²×C₇×#41	1	2	yes	—
629	C₂	—	2	4	no	—
630	C₂	—	2	4	no	—
631	C₂	—	4	2	no	—
632	C₂	—	8	2	no	—
633	C₂	C₇×#3091	1	4	yes	direct product factor
634	C₂	C₂²×C₇×#123	1	1	yes	characteristic
635	C₂	C₂²×C₇×#135	1	1	yes	characteristic
636	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂×C₇×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂⁴×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₇×#117	C₂	semidirect
3. C₇×#3091	C₂	direct (N × H)
4. C₂×C₇×#484	C₂	semidirect
5. C₂×C₇×#481	C₂	semidirect
6. C₂×C₇×#485	C₂	semidirect
7. C₂×C₇×#482	C₂	semidirect
8. C₂×C₇×#483	C₂	semidirect
9. C₂×C₇×#480	C₂	semidirect
10. C₂×C₇×#427	C₂	semidirect
11. C₂×C₇×#416	C₂	semidirect
12. C₂²×C₇×C₂²⋊C₈	C₂	semidirect
32. C₂×C₇×#117	C₂²	semidirect
37. C₇×#485	C₂²	semidirect
38. C₇×#484	C₂²	semidirect
39. C₇×#483	C₂²	semidirect
40. C₇×#482	C₂²	semidirect
41. C₇×#481	C₂²	semidirect
42. C₇×#480	C₂²	semidirect
43. C₇×#427	C₂²	semidirect
44. C₂×C₇×#107	C₂²	semidirect
45. C₂×C₇×#107	C₂²	semidirect
46. C₂×C₇×#106	C₂²	semidirect
47. C₂×C₇×#106	C₂²	semidirect
48. C₇×#416	C₂²	semidirect
49. C₂×C₇×#103	C₂²	semidirect
50. C₂×C₇×#103	C₂²	semidirect
51. C₂×C₇×#102	C₂²	semidirect
52. C₂×C₇×#102	C₂²	semidirect
56. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
57. C₂×#3091	C₇	direct (N × H)
127. C₇×#107	C₂³	semidirect
128. C₇×#107	C₂³	semidirect
129. C₇×#106	C₂³	semidirect
130. C₇×#106	C₂³	semidirect
131. C₇×#103	C₂³	semidirect
132. C₇×#103	C₂³	semidirect
133. C₇×#102	C₂³	semidirect
134. C₇×#102	C₂³	semidirect
139. C₂²×#117	C₂×C₇	semidirect
140. #3091	C₂×C₇	direct (N × H)
141. C₂×#484	C₂×C₇	semidirect
142. C₂×#481	C₂×C₇	semidirect
143. C₂×#485	C₂×C₇	semidirect
144. C₂×#482	C₂×C₇	semidirect
145. C₂×#483	C₂×C₇	semidirect
146. C₂×#480	C₂×C₇	semidirect
147. C₂×#427	C₂×C₇	semidirect
148. C₂×#416	C₂×C₇	semidirect
149. C₂²×C₂²⋊C₈	C₂×C₇	semidirect
250. C₂×#117	C₂²×C₇	semidirect
255. #485	C₂²×C₇	semidirect
256. #484	C₂²×C₇	semidirect
257. #483	C₂²×C₇	semidirect
258. #482	C₂²×C₇	semidirect
259. #481	C₂²×C₇	semidirect
260. #480	C₂²×C₇	semidirect
261. #427	C₂²×C₇	semidirect
262. C₂×#107	C₂²×C₇	semidirect
263. C₂×#107	C₂²×C₇	semidirect
264. C₂×#106	C₂²×C₇	semidirect
265. C₂×#106	C₂²×C₇	semidirect
266. #416	C₂²×C₇	semidirect
267. C₂×#103	C₂²×C₇	semidirect
268. C₂×#103	C₂²×C₇	semidirect
269. C₂×#102	C₂²×C₇	semidirect
270. C₂×#102	C₂²×C₇	semidirect
274. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
405. #107	C₂³×C₇	semidirect
406. #107	C₂³×C₇	semidirect
407. #106	C₂³×C₇	semidirect
408. #106	C₂³×C₇	semidirect
409. #103	C₂³×C₇	semidirect
410. #103	C₂³×C₇	semidirect
411. #102	C₂³×C₇	semidirect
412. #102	C₂³×C₇	semidirect
532. C₂×C₇	#3091	direct (N × H)
597. C₇	C₂×#3091	direct (N × H)
633. C₂	C₇×#3091	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×#525	2
C₂²×C₇×#117	2
C₇×#3091	2
C₂×C₇×#484	2
C₂×C₇×#481	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#483	2
C₂×C₇×#480	2
C₂×C₇×#427	2
C₂×C₇×#416	2
C₂²×C₇×C₂²⋊C₈	2
C₂×#3091	7

Subgroups — C2×C7×#3091 #13237722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3091 #13237722