Subgroups — C₂×C₇×#3233 #13238061

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic
3	C₇×#3233	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×#485	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#482	C₂	1	2	yes	maximal
8	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#533	—	2	4	no	—
14	C₇×#533	C₂²	1	8	yes	complemented
15	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₇×#529	—	2	4	no	—
18	C₇×#529	C₂²	1	8	yes	—
19	C₂×C₇×#126	—	2	1	no	—
20	C₂×C₇×#125	C₂²	1	1	yes	characteristic
21	C₂×C₇×#125	C₂²	1	2	yes	—
22	C₂×C₇×#124	C₂²	1	1	yes	characteristic
23	C₂×C₇×#123	—	2	1	no	—
24	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	—	2	1	no	—
29	C₂×C₄×C₇×Q₈	—	2	1	no	—
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	—	2	1	no	—
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₇×#117	—	2	1	no	—
34	C₂×C₇×#117	C₂²	1	2	yes	—
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×#485	C₂²	1	16	yes	complemented
39	C₇×#482	C₂²	1	16	yes	—
40	C₇×#477	C₂²	1	8	yes	complemented
41	C₇×#476	C₂²	1	8	yes	complemented
42	C₇×#475	C₂²	1	8	yes	complemented
43	C₇×#474	C₂²	1	8	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	1	yes	characteristic
50	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₇×#103	C₂²	1	2	yes	—
52	C₂×C₇×#103	C₂²	1	2	yes	—
53	C₂×C₇×#102	C₂²	1	2	yes	—
54	C₂×C₇×#102	C₂²	1	2	yes	—
55	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
56	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
57	C₂×#3233	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂²×C₇×Q₈	—	2	1	no	—
59	C₂²×C₇×Q₈	—	2	1	no	—
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	—	2	1	no	—
62	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
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×C₄⋊Q₈	—	2	2	no	—
70	C₇×C₄⋊Q₈	—	2	2	no	—
71	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
72	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
73	C₇×#126	—	2	8	no	—
74	C₇×#125	—	2	2	no	—
75	C₇×#125	—	2	4	no	—
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	8	no	—
82	C₇×C₂²⋊Q₈	—	2	8	no	—
83	C₇×C₂²⋊Q₈	—	2	2	no	—
84	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
85	C₇×#121	—	2	2	no	—
86	C₇×#121	C₂³	1	4	yes	—
87	C₄×C₇×Q₈	—	2	8	no	—
88	C₄×C₇×Q₈	—	2	8	no	—
89	C₄×C₇×Q₈	—	2	2	no	—
90	C₄×C₇×Q₈	C₂³	1	4	yes	—
91	C₄×C₇×D₄	—	2	8	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	C₂³	1	4	yes	—
94	C₇×#117	—	2	4	no	—
95	C₇×#117	—	2	8	no	—
96	C₇×#117	C₂³	1	8	yes	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
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	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	2	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₇	—	2	1	no	—
116	C₂×C₄²×C₇	—	2	2	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	4	yes	—
128	C₇×C₄⋊C₈	C₂³	1	4	yes	—
129	C₇×#103	C₂³	1	8	yes	—
130	C₇×#103	C₂³	1	8	yes	—
131	C₇×#102	C₂³	1	8	yes	—
132	C₇×#102	C₂³	1	8	yes	—
133	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
134	C₄×C₇×C₈	C₂³	1	8	yes	—
135	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#529	C₂×C₇	1	1	yes	characteristic
137	#3233	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×#485	C₂×C₇	1	2	yes	complemented
141	C₂×#482	C₂×C₇	1	2	yes	—
142	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
143	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
144	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
145	C₂×#474	C₂×C₇	1	1	yes	characteristic, 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	—	2	4	no	—
152	C₂×C₇×Q₈	—	2	2	no	—
153	C₂×C₇×Q₈	—	2	2	no	—
154	C₂×C₇×Q₈	—	4	4	no	—
155	C₂×C₇×Q₈	—	4	4	no	—
156	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
157	C₂×C₇×D₄	—	2	4	no	—
158	C₂×C₇×D₄	—	2	1	no	—
159	C₂×C₇×D₄	—	2	2	no	—
160	C₂×C₇×D₄	—	2	2	no	—
161	C₂×C₇×D₄	—	4	4	no	—
162	C₂×C₇×D₄	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₇	—	2	4	no	—
164	C₂²×C₄×C₇	—	2	2	no	—
165	C₂²×C₄×C₇	—	2	2	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	2	no	—
169	C₂²×C₄×C₇	—	2	2	no	—
170	C₂²×C₄×C₇	—	2	1	no	—
171	C₂²×C₄×C₇	—	2	4	no	—
172	C₂²×C₄×C₇	—	4	2	no	—
173	C₂²×C₄×C₇	—	4	4	no	—
174	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
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	1	yes	characteristic
179	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
184	C₂×C₇×C₈	—	2	4	no	—
185	C₂×C₇×C₈	—	2	4	no	—
186	C₂×C₇×C₈	C₂⁴	1	4	yes	—
187	C₂×C₇×C₈	C₂⁴	1	4	yes	—
188	C₇×C₄⋊C₄	—	2	4	no	—
189	C₇×C₄⋊C₄	—	2	4	no	—
190	C₇×C₄⋊C₄	—	2	4	no	—
191	C₇×C₄⋊C₄	—	2	8	no	—
192	C₇×C₄⋊C₄	—	2	8	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	2	no	—
197	C₇×C₄⋊C₄	—	2	2	no	—
198	C₇×C₄⋊C₄	—	2	1	no	—
199	C₇×C₄⋊C₄	—	2	1	no	—
200	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
201	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
202	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
203	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
204	C₇×C₂²⋊C₄	—	2	8	no	—
205	C₇×C₂²⋊C₄	—	2	4	no	—
206	C₇×C₂²⋊C₄	—	2	4	no	—
207	C₇×C₂²⋊C₄	—	2	4	no	—
208	C₇×C₂²⋊C₄	—	2	4	no	—
209	C₇×C₂²⋊C₄	—	2	4	no	—
210	C₄²×C₇	—	2	4	no	—
211	C₄²×C₇	—	2	8	no	—
212	C₄²×C₇	C₂×D₄	1	4	yes	—
213	C₄²×C₇	C₂×D₄	1	2	yes	—
214	C₄²×C₇	C₂×D₄	1	4	yes	—
215	C₄²×C₇	C₂×D₄	1	2	yes	—
216	C₄²×C₇	C₂⁴	1	2	yes	—
217	C₄²×C₇	C₂⁴	1	2	yes	—
218	#533	—	2	4	no	—
219	#533	C₂²×C₇	1	8	yes	complemented
220	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
222	#529	—	2	4	no	—
223	#529	C₂²×C₇	1	8	yes	—
224	C₂×#126	—	2	1	no	—
225	C₂×#125	C₂²×C₇	1	2	yes	—
226	C₂×#125	C₂²×C₇	1	1	yes	characteristic
227	C₂×#124	C₂²×C₇	1	1	yes	characteristic
228	C₂×#123	—	2	1	no	—
229	C₂×C₂²⋊Q₈	—	2	1	no	—
230	C₂×C₂²⋊Q₈	—	2	1	no	—
231	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
232	C₂×#121	C₂²×C₇	1	1	yes	characteristic
233	C₂×C₄×Q₈	—	2	1	no	—
234	C₂×C₄×Q₈	—	2	1	no	—
235	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
236	C₂×C₄×D₄	—	2	1	no	—
237	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
238	C₂×#117	—	2	1	no	—
239	C₂×#117	C₂²×C₇	1	2	yes	—
240	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
241	#499	C₂²×C₇	1	16	yes	complemented
242	#488	C₂²×C₇	1	16	yes	complemented
243	#485	C₂²×C₇	1	16	yes	complemented
244	#482	C₂²×C₇	1	16	yes	—
245	#477	C₂²×C₇	1	8	yes	complemented
246	#476	C₂²×C₇	1	8	yes	complemented
247	#475	C₂²×C₇	1	8	yes	complemented
248	#474	C₂²×C₇	1	8	yes	complemented
249	#431	C₂²×C₇	1	8	yes	complemented
250	C₂×#107	C₂²×C₇	1	2	yes	—
251	C₂×#107	C₂²×C₇	1	2	yes	—
252	C₂×#106	C₂²×C₇	1	2	yes	—
253	C₂×#106	C₂²×C₇	1	2	yes	—
254	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
256	C₂×#103	C₂²×C₇	1	2	yes	—
257	C₂×#103	C₂²×C₇	1	2	yes	—
258	C₂×#102	C₂²×C₇	1	2	yes	—
259	C₂×#102	C₂²×C₇	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
261	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
262	C₂³×C₇	—	2	2	no	—
263	C₂³×C₇	—	2	2	no	—
264	C₂³×C₇	—	2	2	no	—
265	C₂³×C₇	—	2	2	no	—
266	C₂³×C₇	—	4	2	no	—
267	C₂³×C₇	—	4	2	no	—
268	C₂³×C₇	—	4	2	no	—
269	C₂³×C₇	C₂²×D₄	1	2	yes	—
270	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
271	C₇×Q₈	—	2	2	no	—
272	C₇×Q₈	—	2	2	no	—
273	C₇×Q₈	—	4	8	no	—
274	C₇×Q₈	—	4	2	no	—
275	C₇×Q₈	—	4	8	no	—
276	C₇×D₄	—	2	2	no	—
277	C₇×D₄	—	2	2	no	—
278	C₇×D₄	—	4	8	no	—
279	C₇×D₄	—	4	2	no	—
280	C₂×C₄×C₇	—	2	2	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	8	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	4	no	—
291	C₂×C₄×C₇	—	2	4	no	—
292	C₂×C₄×C₇	—	2	2	no	—
293	C₂×C₄×C₇	—	4	4	no	—
294	C₂×C₄×C₇	—	4	2	no	—
295	C₂×C₄×C₇	—	4	2	no	—
296	C₂×C₄×C₇	—	4	4	no	—
297	C₂×C₄×C₇	—	4	2	no	—
298	C₂×C₄×C₇	—	4	4	no	—
299	C₂×C₄×C₇	—	4	8	no	—
300	C₂×C₄×C₇	#135	1	4	yes	—
301	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
308	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
309	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
310	C₇×C₈	—	2	4	no	—
311	C₇×C₈	—	2	4	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
319	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₇	1	2	yes	—
322	C₂²×C₈	C₂³×C₇	1	2	yes	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
326	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
327	#126	—	2	8	no	—
328	#125	—	2	2	no	—
329	#125	—	2	4	no	—
330	#125	C₂³×C₇	1	4	yes	—
331	#125	C₂³×C₇	1	8	yes	—
332	#124	—	2	2	no	—
333	#124	C₂³×C₇	1	4	yes	—
334	#123	—	2	8	no	—
335	C₂²⋊Q₈	—	2	8	no	—
336	C₂²⋊Q₈	—	2	8	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
339	#121	—	2	2	no	—
340	#121	C₂³×C₇	1	4	yes	—
341	C₄×Q₈	—	2	8	no	—
342	C₄×Q₈	—	2	8	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	C₂³×C₇	1	4	yes	—
345	C₄×D₄	—	2	8	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	C₂³×C₇	1	4	yes	—
348	#117	—	2	4	no	—
349	#117	—	2	8	no	—
350	#117	C₂³×C₇	1	8	yes	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
372	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
373	C₂×C₄²	C₇×D₄	1	4	yes	—
374	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₇	1	4	yes	—
377	#107	C₂³×C₇	1	8	yes	—
378	#107	C₂³×C₇	1	8	yes	—
379	#106	C₂³×C₇	1	8	yes	—
380	#106	C₂³×C₇	1	8	yes	—
381	C₄⋊C₈	C₂³×C₇	1	4	yes	—
382	C₄⋊C₈	C₂³×C₇	1	4	yes	—
383	#103	C₂³×C₇	1	8	yes	—
384	#103	C₂³×C₇	1	8	yes	—
385	#102	C₂³×C₇	1	8	yes	—
386	#102	C₂³×C₇	1	8	yes	—
387	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
388	C₄×C₈	C₂³×C₇	1	8	yes	—
389	C₂²×C₇	—	2	2	no	—
390	C₂²×C₇	—	2	2	no	—
391	C₂²×C₇	—	2	2	no	—
392	C₂²×C₇	—	4	4	no	—
393	C₂²×C₇	—	4	2	no	—
394	C₂²×C₇	—	4	2	no	—
395	C₂²×C₇	—	4	2	no	—
396	C₂²×C₇	—	8	4	no	—
397	C₂²×C₇	#536	1	2	yes	—
398	C₂²×C₇	C₂×#135	1	2	yes	—
399	C₂²×C₇	#575	1	2	yes	—
400	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
401	C₄×C₇	—	2	2	no	—
402	C₄×C₇	—	2	2	no	—
403	C₄×C₇	—	2	2	no	—
404	C₄×C₇	—	2	2	no	—
405	C₄×C₇	—	4	2	no	—
406	C₄×C₇	—	4	2	no	—
407	C₄×C₇	—	4	4	no	—
408	C₄×C₇	—	4	2	no	—
409	C₄×C₇	—	4	4	no	—
410	C₄×C₇	#536	1	2	yes	—
411	C₄×C₇	C₂×#135	1	4	yes	—
412	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
413	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
414	C₂⁴	—	2	1	no	—
415	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	4	4	no	—
422	C₂×Q₈	—	4	4	no	—
423	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	C₂⁴×C₇	1	2	yes	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
443	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
447	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
448	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
451	C₂×C₈	—	2	4	no	—
452	C₂×C₈	—	2	4	no	—
453	C₂×C₈	C₂⁴×C₇	1	4	yes	—
454	C₂×C₈	C₂⁴×C₇	1	4	yes	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
468	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
470	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₄²	—	2	4	no	—
478	C₄²	—	2	8	no	—
479	C₄²	C₂×C₇×D₄	1	4	yes	—
480	C₄²	C₂×C₇×D₄	1	2	yes	—
481	C₄²	C₂×C₇×D₄	1	4	yes	—
482	C₄²	C₂×C₇×D₄	1	2	yes	—
483	C₄²	C₂⁴×C₇	1	2	yes	—
484	C₄²	C₂⁴×C₇	1	2	yes	—
485	C₂×C₇	—	4	2	no	—
486	C₂×C₇	—	8	2	no	—
487	C₂×C₇	#3233	1	4	yes	direct product factor
488	C₂×C₇	C₂×#536	1	1	yes	characteristic
489	C₂×C₇	C₂²×#135	1	1	yes	characteristic
490	C₂×C₇	C₂×#575	1	1	yes	characteristic
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	C₂²×C₇×D₄	1	2	yes	—
499	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
500	Q₈	—	2	2	no	—
501	Q₈	—	2	2	no	—
502	Q₈	—	4	8	no	—
503	Q₈	—	4	2	no	—
504	Q₈	—	4	8	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	2	no	—
507	D₄	—	4	8	no	—
508	D₄	—	4	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	8	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	8	no	—
529	C₂×C₄	C₇×#135	1	4	yes	—
530	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
531	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
532	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
533	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
534	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
535	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
536	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
537	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
538	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
539	C₈	—	2	4	no	—
540	C₈	—	2	4	no	—
541	C₇	C₂×#3233	1	1	yes	characteristic, direct product factor, Sylow
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	4	no	—
550	C₂²	C₇×#536	1	2	yes	—
551	C₂²	C₂×C₇×#135	1	2	yes	—
552	C₂²	C₇×#575	1	2	yes	—
553	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	2	no	—
563	C₄	C₇×#536	1	2	yes	—
564	C₄	C₂×C₇×#135	1	4	yes	—
565	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
566	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
567	C₂	—	4	2	no	—
568	C₂	—	8	2	no	—
569	C₂	C₇×#3233	1	4	yes	direct product factor
570	C₂	C₂×C₇×#536	1	1	yes	characteristic
571	C₂	C₂²×C₇×#135	1	1	yes	characteristic
572	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
1. C₂×C₇×#533	C₂	semidirect
3. C₇×#3233	C₂	direct (N × H)
4. C₂×C₇×#499	C₂	semidirect
5. C₂×C₇×#488	C₂	semidirect
6. C₂×C₇×#485	C₂	semidirect
8. C₂×C₇×#477	C₂	semidirect
9. C₂×C₇×#475	C₂	semidirect
10. C₂×C₇×#476	C₂	semidirect
11. C₂×C₇×#474	C₂	semidirect
12. C₂×C₇×#431	C₂	semidirect
14. C₇×#533	C₂²	semidirect
36. C₇×#499	C₂²	semidirect
37. C₇×#488	C₂²	semidirect
38. C₇×#485	C₂²	semidirect
40. C₇×#477	C₂²	semidirect
41. C₇×#476	C₂²	semidirect
42. C₇×#475	C₂²	semidirect
43. C₇×#474	C₂²	semidirect
44. C₇×#431	C₂²	semidirect
57. C₂×#3233	C₇	direct (N × H)
135. C₂×#533	C₂×C₇	semidirect
137. #3233	C₂×C₇	direct (N × H)
138. C₂×#499	C₂×C₇	semidirect
139. C₂×#488	C₂×C₇	semidirect
140. C₂×#485	C₂×C₇	semidirect
142. C₂×#477	C₂×C₇	semidirect
143. C₂×#475	C₂×C₇	semidirect
144. C₂×#476	C₂×C₇	semidirect
145. C₂×#474	C₂×C₇	semidirect
146. C₂×#431	C₂×C₇	semidirect
219. #533	C₂²×C₇	semidirect
241. #499	C₂²×C₇	semidirect
242. #488	C₂²×C₇	semidirect
243. #485	C₂²×C₇	semidirect
245. #477	C₂²×C₇	semidirect
246. #476	C₂²×C₇	semidirect
247. #475	C₂²×C₇	semidirect
248. #474	C₂²×C₇	semidirect
249. #431	C₂²×C₇	semidirect
487. C₂×C₇	#3233	direct (N × H)
541. C₇	C₂×#3233	direct (N × H)
569. C₂	C₇×#3233	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×#533	2
C₂×C₇×#529	2
C₇×#3233	2
C₂×C₇×#499	2
C₂×C₇×#488	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#477	2
C₂×C₇×#475	2
C₂×C₇×#476	2
C₂×C₇×#474	2
C₂×C₇×#431	2
C₂×#3233	7

Subgroups — C2×C7×#3233 #13238061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3233 #13238061