Subgroups — C₂×C₇×#3232 #13238056

Order 1792.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 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
2	C₂²×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3232	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#499	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#484	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#481	C₂	1	1	yes	maximal, characteristic
8	C₂×C₇×#483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#480	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×#479	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#529	—	2	4	no	—
14	C₇×#529	C₂²	1	8	yes	—
15	C₂×C₇×#126	—	2	1	no	—
16	C₂×C₇×#125	—	2	1	no	—
17	C₂×C₇×#125	—	2	1	no	—
18	C₂×C₇×#125	—	2	4	no	—
19	C₂×C₇×#125	C₂²	1	1	yes	characteristic
20	C₂×C₇×#125	C₂²	1	2	yes	—
21	C₂×C₇×#125	C₂²	1	2	yes	—
22	C₂×C₇×#125	C₂²	1	8	yes	complemented
23	C₂×C₇×#124	C₂²	1	1	yes	characteristic
24	C₂×C₇×#123	—	2	1	no	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×D₄	—	2	1	no	—
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	—	2	1	no	—
31	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
32	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
33	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
36	C₇×#499	C₂²	1	16	yes	complemented
37	C₇×#488	C₂²	1	16	yes	complemented
38	C₇×#484	C₂²	1	8	yes	complemented
39	C₇×#483	C₂²	1	8	yes	complemented
40	C₇×#481	C₂²	1	8	yes	—
41	C₇×#480	C₂²	1	8	yes	—
42	C₇×#479	C₂²	1	16	yes	complemented
43	C₇×#478	C₂²	1	16	yes	complemented
44	C₇×#431	C₂²	1	8	yes	complemented
45	C₂×C₇×#107	C₂²	1	2	yes	—
46	C₂×C₇×#107	C₂²	1	2	yes	—
47	C₂×C₇×#106	C₂²	1	2	yes	—
48	C₂×C₇×#106	C₂²	1	2	yes	—
49	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
50	C₂×C₇×#103	C₂²	1	2	yes	—
51	C₂×C₇×#103	C₂²	1	2	yes	—
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×#102	C₂²	1	2	yes	—
54	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
57	C₂×#3232	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×D₄	—	2	1	no	—
60	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₇	—	2	1	no	—
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂³×C₄×C₇	—	2	1	no	—
64	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	2	yes	—
68	C₂²×C₇×C₈	C₂³	1	2	yes	—
69	C₇×#126	—	2	8	no	—
70	C₇×#125	—	2	4	no	—
71	C₇×#125	—	2	4	no	—
72	C₇×#125	—	2	8	no	—
73	C₇×#125	—	2	8	no	—
74	C₇×#125	—	2	2	no	—
75	C₇×#125	C₂³	1	8	yes	—
76	C₇×#125	C₂³	1	8	yes	—
77	C₇×#125	C₂³	1	4	yes	—
78	C₇×#124	—	2	2	no	—
79	C₇×#124	C₂³	1	4	yes	—
80	C₇×#123	—	2	8	no	—
81	C₇×C₂²⋊Q₈	—	2	2	no	—
82	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
83	C₇×#121	—	2	2	no	—
84	C₇×#121	C₂³	1	4	yes	—
85	C₄×C₇×Q₈	—	2	2	no	—
86	C₄×C₇×Q₈	C₂³	1	4	yes	—
87	C₄×C₇×D₄	—	2	8	no	—
88	C₄×C₇×D₄	—	2	2	no	—
89	C₄×C₇×D₄	C₂³	1	4	yes	—
90	C₇×#117	—	2	8	no	—
91	C₂×C₇×C₄⋊C₄	—	2	2	no	—
92	C₂×C₇×C₄⋊C₄	—	2	2	no	—
93	C₂×C₇×C₄⋊C₄	—	2	2	no	—
94	C₂×C₇×C₄⋊C₄	—	2	2	no	—
95	C₂×C₇×C₄⋊C₄	—	2	8	no	—
96	C₂×C₇×C₄⋊C₄	—	2	8	no	—
97	C₂×C₇×C₄⋊C₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	2	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₄²×C₇	—	2	1	no	—
117	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₇	D₄	1	4	yes	—
120	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₇	C₂³	1	4	yes	—
123	C₇×#107	C₂³	1	8	yes	—
124	C₇×#107	C₂³	1	8	yes	—
125	C₇×#106	C₂³	1	8	yes	—
126	C₇×#106	C₂³	1	8	yes	—
127	C₇×C₄⋊C₈	C₂³	1	8	yes	—
128	C₇×#103	C₂³	1	8	yes	—
129	C₇×#103	C₂³	1	8	yes	—
130	C₇×#102	C₂³	1	8	yes	—
131	C₇×#102	C₂³	1	8	yes	—
132	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
133	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
134	C₄×C₇×C₈	C₂³	1	8	yes	—
135	C₂×#529	C₂×C₇	1	1	yes	characteristic
136	C₂²×#125	C₂×C₇	1	1	yes	characteristic, complemented
137	#3232	C₂×C₇	1	16	yes	direct product factor
138	C₂×#499	C₂×C₇	1	2	yes	complemented
139	C₂×#488	C₂×C₇	1	2	yes	complemented
140	C₂×#484	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×#481	C₂×C₇	1	1	yes	characteristic
142	C₂×#483	C₂×C₇	1	1	yes	characteristic, complemented
143	C₂×#480	C₂×C₇	1	1	yes	characteristic
144	C₂×#479	C₂×C₇	1	2	yes	complemented
145	C₂×#478	C₂×C₇	1	2	yes	complemented
146	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂⁴×C₇	—	2	1	no	—
148	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₇×Q₈	—	2	1	no	—
150	C₂×C₇×Q₈	—	2	4	no	—
151	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
152	C₂×C₇×D₄	—	2	4	no	—
153	C₂×C₇×D₄	—	2	1	no	—
154	C₂×C₇×D₄	—	2	4	no	—
155	C₂×C₇×D₄	—	4	4	no	—
156	C₂×C₇×D₄	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₇	—	2	4	no	—
158	C₂²×C₄×C₇	—	2	4	no	—
159	C₂²×C₄×C₇	—	2	4	no	—
160	C₂²×C₄×C₇	—	2	4	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	2	no	—
165	C₂²×C₄×C₇	—	2	2	no	—
166	C₂²×C₄×C₇	—	2	4	no	—
167	C₂²×C₄×C₇	—	4	2	no	—
168	C₂²×C₄×C₇	—	4	4	no	—
169	C₂²×C₄×C₇	—	4	4	no	—
170	C₂²×C₄×C₇	—	4	4	no	—
171	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
181	C₂×C₇×C₈	—	2	4	no	—
182	C₂×C₇×C₈	—	2	4	no	—
183	C₂×C₇×C₈	C₂⁴	1	4	yes	—
184	C₂×C₇×C₈	C₂⁴	1	4	yes	—
185	C₇×C₄⋊C₄	—	2	8	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	4	no	—
190	C₇×C₄⋊C₄	—	2	4	no	—
191	C₇×C₄⋊C₄	—	2	2	no	—
192	C₇×C₄⋊C₄	—	2	2	no	—
193	C₇×C₄⋊C₄	—	2	4	no	—
194	C₇×C₄⋊C₄	—	2	4	no	—
195	C₇×C₄⋊C₄	—	2	4	no	—
196	C₇×C₄⋊C₄	—	2	4	no	—
197	C₇×C₄⋊C₄	—	2	1	no	—
198	C₇×C₄⋊C₄	—	2	1	no	—
199	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
201	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
202	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
203	C₇×C₂²⋊C₄	—	2	4	no	—
204	C₇×C₂²⋊C₄	—	2	4	no	—
205	C₇×C₂²⋊C₄	—	2	4	no	—
206	C₇×C₂²⋊C₄	—	2	4	no	—
207	C₇×C₂²⋊C₄	—	2	4	no	—
208	C₄²×C₇	—	2	4	no	—
209	C₄²×C₇	C₂×D₄	1	4	yes	—
210	C₄²×C₇	C₂×D₄	1	2	yes	—
211	C₄²×C₇	C₂×D₄	1	2	yes	—
212	C₄²×C₇	C₂×D₄	1	4	yes	—
213	C₄²×C₇	C₂⁴	1	2	yes	—
214	C₄²×C₇	C₂⁴	1	2	yes	—
215	#529	—	2	4	no	—
216	#529	C₂²×C₇	1	8	yes	—
217	C₂×#126	—	2	1	no	—
218	C₂×#125	—	2	1	no	—
219	C₂×#125	—	2	1	no	—
220	C₂×#125	—	2	4	no	—
221	C₂×#125	C₂²×C₇	1	2	yes	—
222	C₂×#125	C₂²×C₇	1	2	yes	—
223	C₂×#125	C₂²×C₇	1	1	yes	characteristic
224	C₂×#125	C₂²×C₇	1	8	yes	complemented
225	C₂×#124	C₂²×C₇	1	1	yes	characteristic
226	C₂×#123	—	2	1	no	—
227	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
228	C₂×#121	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
232	C₂×#117	—	2	1	no	—
233	C₂²×C₄⋊C₄	—	2	1	no	—
234	C₂²×C₄⋊C₄	—	2	1	no	—
235	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
238	#499	C₂²×C₇	1	16	yes	complemented
239	#488	C₂²×C₇	1	16	yes	complemented
240	#484	C₂²×C₇	1	8	yes	complemented
241	#483	C₂²×C₇	1	8	yes	complemented
242	#481	C₂²×C₇	1	8	yes	—
243	#480	C₂²×C₇	1	8	yes	—
244	#479	C₂²×C₇	1	16	yes	complemented
245	#478	C₂²×C₇	1	16	yes	complemented
246	#431	C₂²×C₇	1	8	yes	complemented
247	C₂×#107	C₂²×C₇	1	2	yes	—
248	C₂×#107	C₂²×C₇	1	2	yes	—
249	C₂×#106	C₂²×C₇	1	2	yes	—
250	C₂×#106	C₂²×C₇	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
252	C₂×#103	C₂²×C₇	1	2	yes	—
253	C₂×#103	C₂²×C₇	1	2	yes	—
254	C₂×#102	C₂²×C₇	1	2	yes	—
255	C₂×#102	C₂²×C₇	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
259	C₂³×C₇	—	2	2	no	—
260	C₂³×C₇	—	2	2	no	—
261	C₂³×C₇	—	2	2	no	—
262	C₂³×C₇	—	4	2	no	—
263	C₂³×C₇	—	4	2	no	—
264	C₂³×C₇	—	4	2	no	—
265	C₂³×C₇	#135	1	4	yes	—
266	C₂³×C₇	C₂²×D₄	1	2	yes	—
267	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
268	C₇×Q₈	—	2	4	no	—
269	C₇×Q₈	—	4	2	no	—
270	C₇×D₄	—	2	4	no	—
271	C₇×D₄	—	4	8	no	—
272	C₇×D₄	—	4	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	8	no	—
275	C₂×C₄×C₇	—	2	2	no	—
276	C₂×C₄×C₇	—	2	2	no	—
277	C₂×C₄×C₇	—	2	2	no	—
278	C₂×C₄×C₇	—	2	2	no	—
279	C₂×C₄×C₇	—	2	4	no	—
280	C₂×C₄×C₇	—	2	4	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	4	no	—
285	C₂×C₄×C₇	—	2	4	no	—
286	C₂×C₄×C₇	—	4	4	no	—
287	C₂×C₄×C₇	—	4	8	no	—
288	C₂×C₄×C₇	—	4	8	no	—
289	C₂×C₄×C₇	—	4	2	no	—
290	C₂×C₄×C₇	—	4	8	no	—
291	C₂×C₄×C₇	—	4	4	no	—
292	C₂×C₄×C₇	—	4	2	no	—
293	C₂×C₄×C₇	—	4	2	no	—
294	C₂×C₄×C₇	—	4	4	no	—
295	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
302	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
303	C₇×C₈	—	2	4	no	—
304	C₇×C₈	—	2	4	no	—
305	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
312	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₇	1	2	yes	—
315	C₂²×C₈	C₂³×C₇	1	2	yes	—
316	#126	—	2	8	no	—
317	#125	—	2	4	no	—
318	#125	—	2	4	no	—
319	#125	—	2	8	no	—
320	#125	—	2	8	no	—
321	#125	—	2	2	no	—
322	#125	C₂³×C₇	1	8	yes	—
323	#125	C₂³×C₇	1	8	yes	—
324	#125	C₂³×C₇	1	4	yes	—
325	#124	—	2	2	no	—
326	#124	C₂³×C₇	1	4	yes	—
327	#123	—	2	8	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
330	#121	—	2	2	no	—
331	#121	C₂³×C₇	1	4	yes	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	C₂³×C₇	1	4	yes	—
334	C₄×D₄	—	2	8	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	C₂³×C₇	1	4	yes	—
337	#117	—	2	8	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	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	8	no	—
343	C₂×C₄⋊C₄	—	2	8	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
356	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
365	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
366	C₂×C₄²	C₇×D₄	1	4	yes	—
367	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₇	1	4	yes	—
370	#107	C₂³×C₇	1	8	yes	—
371	#107	C₂³×C₇	1	8	yes	—
372	#106	C₂³×C₇	1	8	yes	—
373	#106	C₂³×C₇	1	8	yes	—
374	C₄⋊C₈	C₂³×C₇	1	8	yes	—
375	#103	C₂³×C₇	1	8	yes	—
376	#103	C₂³×C₇	1	8	yes	—
377	#102	C₂³×C₇	1	8	yes	—
378	#102	C₂³×C₇	1	8	yes	—
379	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
380	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
381	C₄×C₈	C₂³×C₇	1	8	yes	—
382	C₂²×C₇	—	2	2	no	—
383	C₂²×C₇	—	2	8	no	—
384	C₂²×C₇	—	2	2	no	—
385	C₂²×C₇	—	4	2	no	—
386	C₂²×C₇	—	4	2	no	—
387	C₂²×C₇	—	4	2	no	—
388	C₂²×C₇	—	8	4	no	—
389	C₂²×C₇	#536	1	2	yes	—
390	C₂²×C₇	C₂×#135	1	4	yes	—
391	C₂²×C₇	C₂×#135	1	2	yes	—
392	C₂²×C₇	#575	1	2	yes	—
393	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
394	C₄×C₇	—	2	2	no	—
395	C₄×C₇	—	2	2	no	—
396	C₄×C₇	—	2	2	no	—
397	C₄×C₇	—	2	2	no	—
398	C₄×C₇	—	2	2	no	—
399	C₄×C₇	—	4	2	no	—
400	C₄×C₇	—	4	4	no	—
401	C₄×C₇	—	4	2	no	—
402	C₄×C₇	—	4	2	no	—
403	C₄×C₇	—	4	4	no	—
404	C₄×C₇	#536	1	2	yes	—
405	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	C₂⁴×C₇	1	2	yes	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
433	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
437	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	4	no	—
442	C₂×C₈	C₂⁴×C₇	1	4	yes	—
443	C₂×C₈	C₂⁴×C₇	1	4	yes	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
459	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
460	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
461	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₄²	—	2	4	no	—
468	C₄²	C₂×C₇×D₄	1	4	yes	—
469	C₄²	C₂×C₇×D₄	1	2	yes	—
470	C₄²	C₂×C₇×D₄	1	2	yes	—
471	C₄²	C₂×C₇×D₄	1	4	yes	—
472	C₄²	C₂⁴×C₇	1	2	yes	—
473	C₄²	C₂⁴×C₇	1	2	yes	—
474	C₂×C₇	—	2	4	no	—
475	C₂×C₇	—	8	2	no	—
476	C₂×C₇	#3232	1	4	yes	direct product factor
477	C₂×C₇	C₂×#536	1	1	yes	characteristic
478	C₂×C₇	C₂²×#135	1	1	yes	characteristic
479	C₂×C₇	C₂×#575	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	C₇×#135	1	4	yes	—
487	C₂³	C₂²×C₇×D₄	1	2	yes	—
488	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	4	2	no	—
491	D₄	—	2	4	no	—
492	D₄	—	4	8	no	—
493	D₄	—	4	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	8	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
517	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
518	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
519	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
520	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
521	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
522	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
523	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
524	C₈	—	2	4	no	—
525	C₈	—	2	4	no	—
526	C₇	C₂×#3232	1	1	yes	characteristic, direct product factor, Sylow
527	C₂²	—	2	2	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	8	4	no	—
534	C₂²	C₇×#536	1	2	yes	—
535	C₂²	C₂×C₇×#135	1	4	yes	—
536	C₂²	C₂×C₇×#135	1	2	yes	—
537	C₂²	C₇×#575	1	2	yes	—
538	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	2	no	—
549	C₄	C₇×#536	1	2	yes	—
550	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
551	C₂	—	2	4	no	—
552	C₂	—	8	2	no	—
553	C₂	C₇×#3232	1	4	yes	direct product factor
554	C₂	C₂×C₇×#536	1	1	yes	characteristic
555	C₂	C₂²×C₇×#135	1	1	yes	characteristic
556	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×#121	C₂²
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
2. C₂²×C₇×#125	C₂	semidirect
3. C₇×#3232	C₂	direct (N × H)
4. C₂×C₇×#499	C₂	semidirect
5. C₂×C₇×#488	C₂	semidirect
6. C₂×C₇×#484	C₂	semidirect
8. C₂×C₇×#483	C₂	semidirect
10. C₂×C₇×#479	C₂	semidirect
11. C₂×C₇×#478	C₂	semidirect
12. C₂×C₇×#431	C₂	semidirect
22. C₂×C₇×#125	C₂²	semidirect
36. C₇×#499	C₂²	semidirect
37. C₇×#488	C₂²	semidirect
38. C₇×#484	C₂²	semidirect
39. C₇×#483	C₂²	semidirect
42. C₇×#479	C₂²	semidirect
43. C₇×#478	C₂²	semidirect
44. C₇×#431	C₂²	semidirect
57. C₂×#3232	C₇	direct (N × H)
136. C₂²×#125	C₂×C₇	semidirect
137. #3232	C₂×C₇	direct (N × H)
138. C₂×#499	C₂×C₇	semidirect
139. C₂×#488	C₂×C₇	semidirect
140. C₂×#484	C₂×C₇	semidirect
142. C₂×#483	C₂×C₇	semidirect
144. C₂×#479	C₂×C₇	semidirect
145. C₂×#478	C₂×C₇	semidirect
146. C₂×#431	C₂×C₇	semidirect
224. C₂×#125	C₂²×C₇	semidirect
238. #499	C₂²×C₇	semidirect
239. #488	C₂²×C₇	semidirect
240. #484	C₂²×C₇	semidirect
241. #483	C₂²×C₇	semidirect
244. #479	C₂²×C₇	semidirect
245. #478	C₂²×C₇	semidirect
246. #431	C₂²×C₇	semidirect
476. C₂×C₇	#3232	direct (N × H)
526. C₇	C₂×#3232	direct (N × H)
553. C₂	C₇×#3232	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×C₇×#125	2
C₇×#3232	2
C₂×C₇×#499	2
C₂×C₇×#488	2
C₂×C₇×#484	2
C₂×C₇×#481	2
C₂×C₇×#483	2
C₂×C₇×#480	2
C₂×C₇×#479	2
C₂×C₇×#478	2
C₂×C₇×#431	2
C₂×#3232	7

Subgroups — C2×C7×#3232 #13238056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3232 #13238056