Subgroups — C₂×C₇×#3173 #13237893

Order 1792.

1970 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#542	C₂	1	2	yes	maximal, complemented
2	C₇×#3173	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic
8	C₂×C₇×#465	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₇×#542	—	2	8	no	—
19	C₇×#542	C₂²	1	16	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₇×#126	—	2	2	no	—
22	C₂×C₇×#124	—	2	2	no	—
23	C₂×C₇×#124	C₂²	1	2	yes	—
24	C₂×C₇×#123	—	2	2	no	—
25	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₇×#121	C₂²	1	2	yes	—
28	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
30	C₂×C₇×#117	C₂²	1	1	yes	characteristic
31	C₇×#498	C₂²	1	8	yes	complemented
32	C₇×#495	C₂²	1	8	yes	complemented
33	C₇×#489	C₂²	1	16	yes	complemented
34	C₇×#470	C₂²	1	8	yes	complemented
35	C₇×#469	C₂²	1	8	yes	—
36	C₇×#465	C₂²	1	16	yes	complemented
37	C₇×#442	C₂²	1	8	yes	complemented
38	C₇×#441	C₂²	1	8	yes	complemented
39	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
40	C₂×C₇×#106	C₂²	1	2	yes	—
41	C₂×C₇×#106	C₂²	1	1	yes	characteristic
42	C₂×C₇×#106	C₂²	1	1	yes	characteristic
43	C₂×C₇×#103	C₂²	1	2	yes	—
44	C₂×C₇×#103	C₂²	1	2	yes	—
45	C₂×C₇×#102	C₂²	1	2	yes	—
46	C₂×C₇×#102	C₂²	1	2	yes	—
47	C₇×#405	C₂²	1	8	yes	complemented
48	C₂×C₇×#97	C₂²	1	1	yes	characteristic
49	C₂×C₇×#97	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
52	C₂×#3173	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂²×C₇×Q₈	—	2	2	no	—
54	C₂²×C₇×Q₈	C₂³	1	2	yes	—
55	C₂²×C₇×D₄	—	2	2	no	—
56	C₂²×C₇×D₄	C₂³	1	2	yes	—
57	C₂³×C₄×C₇	—	2	2	no	—
58	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₇×Q₁₆	—	2	4	no	—
60	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
61	C₂×C₇×SD₁₆	—	2	8	no	—
62	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
63	C₂×C₇×D₈	—	2	4	no	—
64	C₂×C₇×D₈	C₂³	1	4	yes	—
65	C₂×C₇×M₁₆	—	2	4	no	—
66	C₂×C₇×M₁₆	C₂³	1	4	yes	—
67	C₂²×C₇×C₈	—	2	4	no	—
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	4	yes	—
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₇×C₄⋊Q₈	—	2	4	no	—
74	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
75	C₇×#126	—	2	16	no	—
76	C₇×#124	—	2	16	no	—
77	C₇×#124	—	2	4	no	—
78	C₇×#124	C₂³	1	8	yes	—
79	C₇×#123	—	2	16	no	—
80	C₇×C₂²⋊Q₈	—	2	4	no	—
81	C₇×C₂²⋊Q₈	—	2	16	no	—
82	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
83	C₇×#121	—	2	4	no	—
84	C₇×#121	C₂³	1	8	yes	—
85	C₄×C₇×Q₈	—	2	4	no	—
86	C₄×C₇×Q₈	C₂³	1	8	yes	—
87	C₄×C₇×D₄	—	2	4	no	—
88	C₄×C₇×D₄	C₂³	1	8	yes	—
89	C₇×#117	D₄	1	4	yes	—
90	C₇×#117	C₂³	1	4	yes	—
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	D₄	1	2	yes	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
103	C₂×C₄²×C₇	—	2	2	no	—
104	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
106	C₇×#106	C₂³	1	4	yes	—
107	C₇×#106	C₂³	1	4	yes	—
108	C₇×#106	C₂³	1	8	yes	—
109	C₇×#103	C₂³	1	8	yes	—
110	C₇×#103	C₂³	1	8	yes	—
111	C₇×#102	C₂³	1	8	yes	—
112	C₇×#102	C₂³	1	8	yes	—
113	C₇×#97	C₂³	1	4	yes	—
114	C₇×#97	C₂³	1	4	yes	—
115	C₄×C₇×C₈	C₂³	1	4	yes	—
116	C₄×C₇×C₈	C₂³	1	4	yes	—
117	C₂×#542	C₂×C₇	1	2	yes	complemented
118	#3173	C₂×C₇	1	16	yes	direct product factor
119	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂×#495	C₂×C₇	1	1	yes	characteristic, complemented
121	C₂×#489	C₂×C₇	1	2	yes	complemented
122	C₂×#470	C₂×C₇	1	1	yes	characteristic, complemented
123	C₂×#469	C₂×C₇	1	1	yes	characteristic
124	C₂×#465	C₂×C₇	1	2	yes	complemented
125	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
127	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	complemented
128	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂⁴×C₇	—	2	2	no	—
130	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₇×Q₈	—	2	2	no	—
132	C₂×C₇×Q₈	—	2	8	no	—
133	C₂×C₇×Q₈	—	2	4	no	—
134	C₂×C₇×Q₈	—	2	4	no	—
135	C₂×C₇×Q₈	—	8	4	no	—
136	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
137	C₂×C₇×D₄	—	2	8	no	—
138	C₂×C₇×D₄	—	2	2	no	—
139	C₂×C₇×D₄	—	2	4	no	—
140	C₂×C₇×D₄	—	2	4	no	—
141	C₂×C₇×D₄	—	8	4	no	—
142	C₂×C₇×D₄	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	2	no	—
145	C₂²×C₄×C₇	—	2	2	no	—
146	C₂²×C₄×C₇	—	2	2	no	—
147	C₂²×C₄×C₇	—	2	2	no	—
148	C₂²×C₄×C₇	—	2	8	no	—
149	C₂²×C₄×C₇	—	8	4	no	—
150	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
156	C₇×Q₁₆	—	2	8	no	—
157	C₇×SD₁₆	—	2	16	no	—
158	C₇×D₈	—	2	8	no	—
159	C₇×M₁₆	—	2	8	no	—
160	C₂×C₇×C₈	—	2	2	no	—
161	C₂×C₇×C₈	—	2	2	no	—
162	C₂×C₇×C₈	—	2	8	no	—
163	C₂×C₇×C₈	#41	1	4	yes	—
164	C₂×C₇×C₈	#41	1	4	yes	—
165	C₂×C₇×C₈	C₂⁴	1	2	yes	—
166	C₂×C₇×C₈	C₂⁴	1	2	yes	—
167	C₂×C₇×C₈	C₂⁴	1	2	yes	—
168	C₂×C₇×C₈	C₂⁴	1	2	yes	—
169	C₇×C₄⋊C₄	—	2	8	no	—
170	C₇×C₄⋊C₄	—	2	8	no	—
171	C₇×C₄⋊C₄	—	2	8	no	—
172	C₇×C₄⋊C₄	—	2	2	no	—
173	C₇×C₄⋊C₄	—	2	2	no	—
174	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
175	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
176	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
177	C₇×C₂²⋊C₄	—	2	8	no	—
178	C₇×C₂²⋊C₄	—	2	8	no	—
179	C₇×C₂²⋊C₄	—	2	8	no	—
180	C₇×C₂²⋊C₄	—	2	8	no	—
181	C₇×C₂²⋊C₄	—	2	8	no	—
182	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
183	C₄²×C₇	—	2	8	no	—
184	C₄²×C₇	C₂×D₄	1	2	yes	—
185	C₄²×C₇	C₂×D₄	1	2	yes	—
186	C₄²×C₇	C₂⁴	1	2	yes	—
187	C₄²×C₇	C₂⁴	1	2	yes	—
188	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
189	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
190	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
191	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
192	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
193	#542	—	2	8	no	—
194	#542	C₂²×C₇	1	16	yes	complemented
195	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
196	C₂×#126	—	2	2	no	—
197	C₂×#124	—	2	2	no	—
198	C₂×#124	C₂²×C₇	1	2	yes	—
199	C₂×#123	—	2	2	no	—
200	C₂×C₂²⋊Q₈	—	2	2	no	—
201	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
202	C₂×#121	C₂²×C₇	1	2	yes	—
203	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
204	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
205	C₂×#117	C₂²×C₇	1	1	yes	characteristic
206	#498	C₂²×C₇	1	8	yes	complemented
207	#495	C₂²×C₇	1	8	yes	complemented
208	#489	C₂²×C₇	1	16	yes	complemented
209	#470	C₂²×C₇	1	8	yes	complemented
210	#469	C₂²×C₇	1	8	yes	—
211	#465	C₂²×C₇	1	16	yes	complemented
212	#442	C₂²×C₇	1	8	yes	complemented
213	#441	C₂²×C₇	1	8	yes	complemented
214	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
215	C₂×#106	C₂²×C₇	1	2	yes	—
216	C₂×#106	C₂²×C₇	1	1	yes	characteristic
217	C₂×#106	C₂²×C₇	1	1	yes	characteristic
218	C₂×#103	C₂²×C₇	1	2	yes	—
219	C₂×#103	C₂²×C₇	1	2	yes	—
220	C₂×#102	C₂²×C₇	1	2	yes	—
221	C₂×#102	C₂²×C₇	1	2	yes	—
222	#405	C₂²×C₇	1	8	yes	complemented
223	C₂×#97	C₂²×C₇	1	1	yes	characteristic
224	C₂×#97	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
227	C₂³×C₇	—	2	2	no	—
228	C₂³×C₇	—	2	4	no	—
229	C₂³×C₇	—	2	4	no	—
230	C₂³×C₇	—	4	4	no	—
231	C₂³×C₇	—	4	4	no	—
232	C₂³×C₇	—	4	4	no	—
233	C₂³×C₇	C₂²×D₄	1	2	yes	—
234	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
235	C₇×Q₈	—	2	4	no	—
236	C₇×Q₈	—	2	4	no	—
237	C₇×Q₈	—	4	4	no	—
238	C₇×Q₈	—	8	8	no	—
239	C₇×D₄	—	2	4	no	—
240	C₇×D₄	—	2	4	no	—
241	C₇×D₄	—	4	4	no	—
242	C₇×D₄	—	8	8	no	—
243	C₂×C₄×C₇	—	2	2	no	—
244	C₂×C₄×C₇	—	2	4	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	2	4	no	—
247	C₂×C₄×C₇	—	2	2	no	—
248	C₂×C₄×C₇	—	2	2	no	—
249	C₂×C₄×C₇	—	2	4	no	—
250	C₂×C₄×C₇	—	2	4	no	—
251	C₂×C₄×C₇	—	2	4	no	—
252	C₂×C₄×C₇	—	4	4	no	—
253	C₂×C₄×C₇	—	4	4	no	—
254	C₂×C₄×C₇	—	4	4	no	—
255	C₂×C₄×C₇	—	8	8	no	—
256	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
257	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
258	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₇	C₂×#41	1	2	yes	—
261	C₂×C₄×C₇	C₂×#41	1	2	yes	—
262	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
263	C₇×C₈	—	2	2	no	—
264	C₇×C₈	—	2	2	no	—
265	C₇×C₈	C₂×#41	1	4	yes	—
266	C₇×C₈	C₂×#41	1	4	yes	—
267	C₂²×Q₈	—	2	2	no	—
268	C₂²×Q₈	C₂³×C₇	1	2	yes	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	C₂³×C₇	1	2	yes	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
273	C₂×Q₁₆	—	2	4	no	—
274	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
275	C₂×SD₁₆	—	2	8	no	—
276	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
277	C₂×D₈	—	2	4	no	—
278	C₂×D₈	C₂³×C₇	1	4	yes	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	C₂³×C₇	1	4	yes	—
281	C₂²×C₈	—	2	4	no	—
282	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₇	1	4	yes	—
284	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
287	C₄⋊Q₈	—	2	4	no	—
288	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
289	#126	—	2	16	no	—
290	#124	—	2	16	no	—
291	#124	—	2	4	no	—
292	#124	C₂³×C₇	1	8	yes	—
293	#123	—	2	16	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	2	16	no	—
296	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
297	#121	—	2	4	no	—
298	#121	C₂³×C₇	1	8	yes	—
299	C₄×Q₈	—	2	4	no	—
300	C₄×Q₈	C₂³×C₇	1	8	yes	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	C₂³×C₇	1	8	yes	—
303	#117	C₇×D₄	1	4	yes	—
304	#117	C₂³×C₇	1	4	yes	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
320	#106	C₂³×C₇	1	8	yes	—
321	#106	C₂³×C₇	1	4	yes	—
322	#106	C₂³×C₇	1	4	yes	—
323	#103	C₂³×C₇	1	8	yes	—
324	#103	C₂³×C₇	1	8	yes	—
325	#102	C₂³×C₇	1	8	yes	—
326	#102	C₂³×C₇	1	8	yes	—
327	#97	C₂³×C₇	1	4	yes	—
328	#97	C₂³×C₇	1	4	yes	—
329	C₄×C₈	C₂³×C₇	1	4	yes	—
330	C₄×C₈	C₂³×C₇	1	4	yes	—
331	C₂²×C₇	—	2	2	no	—
332	C₂²×C₇	—	2	4	no	—
333	C₂²×C₇	—	4	4	no	—
334	C₂²×C₇	—	4	4	no	—
335	C₂²×C₇	—	4	4	no	—
336	C₂²×C₇	—	4	4	no	—
337	C₂²×C₇	—	8	8	no	—
338	C₂²×C₇	#532	1	2	yes	—
339	C₂²×C₇	#577	1	4	yes	—
340	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
341	C₄×C₇	—	2	2	no	—
342	C₄×C₇	—	2	4	no	—
343	C₄×C₇	—	2	4	no	—
344	C₄×C₇	—	4	4	no	—
345	C₄×C₇	—	4	4	no	—
346	C₄×C₇	—	4	4	no	—
347	C₄×C₇	#532	1	2	yes	—
348	C₄×C₇	C₂²×#41	1	1	yes	characteristic
349	C₄×C₇	C₂²×#41	1	1	yes	characteristic
350	C₂⁴	—	2	2	no	—
351	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	8	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	4	no	—
356	C₂×Q₈	—	8	4	no	—
357	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	8	4	no	—
363	C₂×D₄	C₂⁴×C₇	1	4	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	8	4	no	—
371	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
372	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
373	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
377	Q₁₆	—	2	8	no	—
378	SD₁₆	—	2	16	no	—
379	D₈	—	2	8	no	—
380	M₁₆	—	2	8	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	8	no	—
384	C₂×C₈	C₇×#41	1	4	yes	—
385	C₂×C₈	C₇×#41	1	4	yes	—
386	C₂×C₈	C₂⁴×C₇	1	2	yes	—
387	C₂×C₈	C₂⁴×C₇	1	2	yes	—
388	C₂×C₈	C₂⁴×C₇	1	2	yes	—
389	C₂×C₈	C₂⁴×C₇	1	2	yes	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
396	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
397	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
404	C₄²	—	2	8	no	—
405	C₄²	C₂×C₇×D₄	1	2	yes	—
406	C₄²	C₂×C₇×D₄	1	2	yes	—
407	C₄²	C₂⁴×C₇	1	2	yes	—
408	C₄²	C₂⁴×C₇	1	2	yes	—
409	C₂×C₇	—	4	2	no	—
410	C₂×C₇	—	8	4	no	—
411	C₂×C₇	#3173	1	4	yes	direct product factor
412	C₂×C₇	C₂×#532	1	1	yes	characteristic
413	C₂×C₇	C₂×#577	1	2	yes	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	C₂²×C₇×D₄	1	2	yes	—
421	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
422	Q₈	—	2	4	no	—
423	Q₈	—	2	4	no	—
424	Q₈	—	4	4	no	—
425	Q₈	—	8	8	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	4	no	—
429	D₄	—	8	8	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	8	8	no	—
443	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
444	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
445	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
446	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
447	C₂×C₄	C₂×C₇×#41	1	2	yes	—
448	C₂×C₄	C₂×C₇×#41	1	2	yes	—
449	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	C₂×C₇×#41	1	4	yes	—
453	C₈	C₂×C₇×#41	1	4	yes	—
454	C₇	C₂×#3173	1	1	yes	characteristic, direct product factor, Sylow
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	8	no	—
462	C₂²	C₇×#532	1	2	yes	—
463	C₂²	C₇×#577	1	4	yes	—
464	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
465	C₄	—	2	4	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	4	no	—
471	C₄	C₇×#532	1	2	yes	—
472	C₄	C₂²×C₇×#41	1	1	yes	characteristic
473	C₄	C₂²×C₇×#41	1	1	yes	characteristic
474	C₂	—	4	2	no	—
475	C₂	—	8	4	no	—
476	C₂	C₇×#3173	1	4	yes	direct product factor
477	C₂	C₂×C₇×#532	1	1	yes	characteristic
478	C₂	C₂×C₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#469	C₂
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×#542	C₂	semidirect
2. C₇×#3173	C₂	direct (N × H)
3. C₂×C₇×#498	C₂	semidirect
4. C₂×C₇×#495	C₂	semidirect
5. C₂×C₇×#489	C₂	semidirect
6. C₂×C₇×#470	C₂	semidirect
8. C₂×C₇×#465	C₂	semidirect
9. C₂×C₇×#442	C₂	semidirect
10. C₂×C₇×#441	C₂	semidirect
11. C₂×C₄×C₇×SD₁₆	C₂	semidirect
12. C₂×C₇×#405	C₂	semidirect
19. C₇×#542	C₂²	semidirect
31. C₇×#498	C₂²	semidirect
32. C₇×#495	C₂²	semidirect
33. C₇×#489	C₂²	semidirect
34. C₇×#470	C₂²	semidirect
36. C₇×#465	C₂²	semidirect
37. C₇×#442	C₂²	semidirect
38. C₇×#441	C₂²	semidirect
39. C₄×C₇×SD₁₆	C₂²	semidirect
47. C₇×#405	C₂²	semidirect
52. C₂×#3173	C₇	direct (N × H)
117. C₂×#542	C₂×C₇	semidirect
118. #3173	C₂×C₇	direct (N × H)
119. C₂×#498	C₂×C₇	semidirect
120. C₂×#495	C₂×C₇	semidirect
121. C₂×#489	C₂×C₇	semidirect
122. C₂×#470	C₂×C₇	semidirect
124. C₂×#465	C₂×C₇	semidirect
125. C₂×#442	C₂×C₇	semidirect
126. C₂×#441	C₂×C₇	semidirect
127. C₂×C₄×SD₁₆	C₂×C₇	semidirect
128. C₂×#405	C₂×C₇	semidirect
194. #542	C₂²×C₇	semidirect
206. #498	C₂²×C₇	semidirect
207. #495	C₂²×C₇	semidirect
208. #489	C₂²×C₇	semidirect
209. #470	C₂²×C₇	semidirect
211. #465	C₂²×C₇	semidirect
212. #442	C₂²×C₇	semidirect
213. #441	C₂²×C₇	semidirect
214. C₄×SD₁₆	C₂²×C₇	semidirect
222. #405	C₂²×C₇	semidirect
411. C₂×C₇	#3173	direct (N × H)
454. C₇	C₂×#3173	direct (N × H)
476. C₂	C₇×#3173	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×#542	2
C₇×#3173	2
C₂×C₇×#498	2
C₂×C₇×#495	2
C₂×C₇×#489	2
C₂×C₇×#470	2
C₂×C₇×#469	2
C₂×C₇×#465	2
C₂×C₇×#442	2
C₂×C₇×#441	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₇×#405	2
C₂×#3173	7

Subgroups — C2×C7×#3173 #13237893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3173 #13237893