Subgroups — C₂×C₇×#2956 #13237396

Order 1792.

2674 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#568	C₂	1	2	yes	maximal, complemented
3	C₇×#2956	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#444	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#443	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#430	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₇×#104	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	C₂²	1	2	yes	—
10	C₇×#575	C₄	1	8	yes	complemented
11	C₇×#575	C₂²	1	8	yes	—
12	C₂×C₇×#137	C₄	1	4	yes	complemented
13	C₂×C₇×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
14	C₂×C₇×#135	C₂²	1	4	yes	—
15	C₇×#568	—	2	8	no	—
16	C₇×#568	C₂²	1	16	yes	complemented
17	C₂×C₇×#131	—	2	4	no	—
18	C₂×C₇×#131	C₂²	1	8	yes	complemented
19	C₂²×C₇×M₁₆	—	2	4	no	—
20	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
24	C₇×#444	C₂²	1	32	yes	complemented
25	C₇×#443	C₂²	1	32	yes	complemented
26	C₇×#430	C₂²	1	8	yes	complemented
27	C₂×C₇×#108	C₂²	1	4	yes	complemented
28	C₂×C₇×#104	C₂²	1	4	yes	complemented
29	C₂×C₇×#104	C₂²	1	4	yes	complemented
30	C₂×C₇×#104	C₂²	1	16	yes	complemented
31	C₄×C₇×M₁₆	C₂²	1	8	yes	complemented
32	C₂×C₇×#97	C₂²	1	2	yes	complemented
33	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
34	C₂×#2956	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₇×#41	—	2	2	no	—
36	C₂×C₇×#41	—	2	4	no	—
37	C₂×C₇×#41	—	2	2	no	—
38	C₂×C₇×#41	—	2	4	no	—
39	C₂×C₇×#41	C₂×C₄	1	4	yes	—
40	C₂×C₇×#41	C₂×C₄	1	8	yes	—
41	C₂×C₇×#41	C₂³	1	4	yes	—
42	C₂×C₇×#41	C₂³	1	8	yes	—
43	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
44	C₂²×C₇×D₄	—	2	2	no	—
45	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₇	—	2	2	no	—
47	C₂³×C₄×C₇	—	2	1	no	—
48	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
49	C₇×#137	C₂×C₄	1	32	yes	complemented
50	C₇×AGL(1,ℤ/8)	C₂×C₄	1	32	yes	complemented
51	C₇×#135	C₂×C₄	1	16	yes	complemented
52	C₇×#135	C₂³	1	16	yes	—
53	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
54	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	complemented
55	C₂×C₇×D₈	C₂×C₄	1	4	yes	complemented
56	C₇×#131	—	2	32	no	—
57	C₇×#131	—	2	16	no	—
58	C₇×#131	C₂³	1	32	yes	complemented
59	C₂×C₇×M₁₆	—	2	2	no	—
60	C₂×C₇×M₁₆	—	2	4	no	—
61	C₂×C₇×M₁₆	—	2	32	no	—
62	C₂×C₇×M₁₆	—	2	8	no	—
63	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
64	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
65	C₂×C₇×M₁₆	D₄	1	4	yes	—
66	C₂×C₇×M₁₆	D₄	1	4	yes	—
67	C₂×C₇×M₁₆	C₂³	1	4	yes	—
68	C₂×C₇×M₁₆	C₂³	1	8	yes	—
69	C₂×C₇×M₁₆	C₂³	1	4	yes	—
70	C₂×C₇×M₁₆	C₂³	1	4	yes	—
71	C₂²×C₇×C₈	—	2	2	no	—
72	C₂²×C₇×C₈	—	2	8	no	—
73	C₂²×C₇×C₈	C₂³	1	2	yes	—
74	C₂²×C₇×C₈	C₂³	1	2	yes	—
75	C₂×C₄²×C₇	—	2	1	no	—
76	C₂×C₄²×C₇	—	2	2	no	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	4	yes	—
80	C₇×#108	C₂³	1	16	yes	complemented
81	C₇×#104	C₂³	1	16	yes	complemented
82	C₇×#104	C₂³	1	16	yes	complemented
83	C₇×#97	C₂³	1	8	yes	complemented
84	C₄×C₇×C₈	C₂³	1	8	yes	complemented
85	C₂×#575	C₂×C₇	1	1	yes	characteristic
86	C₂×#568	C₂×C₇	1	2	yes	complemented
87	#2956	C₂×C₇	1	16	yes	direct product factor
88	C₂×#444	C₂×C₇	1	4	yes	complemented
89	C₂×#443	C₂×C₇	1	4	yes	complemented
90	C₂×#430	C₂×C₇	1	1	yes	characteristic, complemented
91	C₂²×#104	C₂×C₇	1	2	yes	complemented
92	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
93	C₂⁴×C₇	—	2	2	no	—
94	C₂⁴×C₇	#41	1	1	yes	characteristic
95	C₇×#41	—	2	8	no	—
96	C₇×#41	—	2	8	no	—
97	C₇×#41	—	2	8	no	—
98	C₇×#41	—	2	8	no	—
99	C₇×#41	—	2	4	no	—
100	C₇×#41	—	2	4	no	—
101	C₇×#41	—	2	8	no	—
102	C₇×#41	C₂²×C₄	1	8	yes	—
103	C₇×#41	C₂²×C₄	1	16	yes	—
104	C₇×#41	C₂⁴	1	8	yes	—
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂×C₇×Q₈	—	2	4	no	—
107	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
108	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
109	C₂×C₇×D₄	—	2	4	no	—
110	C₂×C₇×D₄	—	2	8	no	—
111	C₂×C₇×D₄	—	2	4	no	—
112	C₂×C₇×D₄	—	2	8	no	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	2	4	no	—
115	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
116	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	1	no	—
119	C₂²×C₄×C₇	—	2	4	no	—
120	C₂²×C₄×C₇	—	2	8	no	—
121	C₂²×C₄×C₇	—	2	8	no	—
122	C₂²×C₄×C₇	—	2	4	no	—
123	C₂²×C₄×C₇	—	2	4	no	—
124	C₂²×C₄×C₇	—	2	1	no	—
125	C₂²×C₄×C₇	—	4	4	no	—
126	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇	#41	1	1	yes	characteristic
131	C₂²×C₄×C₇	#41	1	2	yes	—
132	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
134	C₇×Q₁₆	C₂²×C₄	1	16	yes	complemented
135	C₇×SD₁₆	C₂²×C₄	1	32	yes	complemented
136	C₇×D₈	C₂²×C₄	1	16	yes	complemented
137	C₇×M₁₆	—	2	8	no	—
138	C₇×M₁₆	—	2	4	no	—
139	C₇×M₁₆	—	2	32	no	—
140	C₇×M₁₆	C₂²×C₄	1	16	yes	—
141	C₇×M₁₆	C₂×D₄	1	16	yes	—
142	C₇×M₁₆	C₂⁴	1	8	yes	—
143	C₂×C₇×C₈	—	2	8	no	—
144	C₂×C₇×C₈	—	2	4	no	—
145	C₂×C₇×C₈	—	2	32	no	—
146	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
147	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
148	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
149	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
150	C₂×C₇×C₈	C₂⁴	1	4	yes	—
151	C₂×C₇×C₈	C₂⁴	1	4	yes	—
152	C₄²×C₇	—	2	1	no	—
153	C₄²×C₇	—	2	4	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	C₂⁴	1	2	yes	—
156	C₄²×C₇	C₂⁴	1	2	yes	—
157	C₂²×#41	C₂²×C₇	1	2	yes	—
158	#575	C₄×C₇	1	8	yes	complemented
159	#575	C₂²×C₇	1	8	yes	—
160	C₂×#137	C₄×C₇	1	4	yes	complemented
161	C₂×AGL(1,ℤ/8)	C₄×C₇	1	4	yes	complemented
162	C₂×#135	C₂²×C₇	1	4	yes	—
163	#568	—	2	8	no	—
164	#568	C₂²×C₇	1	16	yes	complemented
165	C₂×#131	—	2	4	no	—
166	C₂×#131	C₂²×C₇	1	8	yes	complemented
167	C₂²×M₁₆	—	2	4	no	—
168	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
169	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
170	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
171	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
172	#444	C₂²×C₇	1	32	yes	complemented
173	#443	C₂²×C₇	1	32	yes	complemented
174	#430	C₂²×C₇	1	8	yes	complemented
175	C₂×#108	C₂²×C₇	1	4	yes	complemented
176	C₂×#104	C₂²×C₇	1	4	yes	complemented
177	C₂×#104	C₂²×C₇	1	4	yes	complemented
178	C₂×#104	C₂²×C₇	1	16	yes	complemented
179	C₄×M₁₆	C₂²×C₇	1	8	yes	complemented
180	C₂×#97	C₂²×C₇	1	2	yes	complemented
181	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
182	C₂³×C₇	—	2	4	no	—
183	C₂³×C₇	—	2	8	no	—
184	C₂³×C₇	—	4	2	no	—
185	C₂³×C₇	—	8	4	no	—
186	C₂³×C₇	C₄×D₄	1	2	yes	—
187	C₂³×C₇	C₄×D₄	1	2	yes	—
188	C₂³×C₇	C₂×#41	1	1	yes	characteristic
189	C₂³×C₇	C₂×#41	1	2	yes	—
190	C₇×Q₈	—	2	8	no	—
191	C₇×Q₈	—	2	4	no	—
192	C₇×Q₈	C₂³×C₄	1	8	yes	—
193	C₇×D₄	—	2	16	no	—
194	C₇×D₄	—	2	8	no	—
195	C₇×D₄	—	2	8	no	—
196	C₇×D₄	—	2	8	no	—
197	C₇×D₄	—	2	4	no	—
198	C₇×D₄	C₂³×C₄	1	8	yes	—
199	C₂×C₄×C₇	—	2	4	no	—
200	C₂×C₄×C₇	—	2	8	no	—
201	C₂×C₄×C₇	—	2	4	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	2	8	no	—
204	C₂×C₄×C₇	—	2	16	no	—
205	C₂×C₄×C₇	—	2	8	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	4	8	no	—
208	C₂×C₄×C₇	—	4	2	no	—
209	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
211	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
212	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
216	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₇	C₂×#41	1	2	yes	—
221	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
222	C₇×C₈	—	2	8	no	—
223	C₇×C₈	C₂³×C₄	1	8	yes	—
224	C₇×C₈	C₂²×D₄	1	8	yes	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	4	no	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	2	4	no	—
229	C₂×#41	C₂×C₄×C₇	1	4	yes	—
230	C₂×#41	C₂×C₄×C₇	1	8	yes	—
231	C₂×#41	C₂³×C₇	1	4	yes	—
232	C₂×#41	C₂³×C₇	1	8	yes	—
233	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
239	#137	C₂×C₄×C₇	1	32	yes	complemented
240	AGL(1,ℤ/8)	C₂×C₄×C₇	1	32	yes	complemented
241	#135	C₂×C₄×C₇	1	16	yes	complemented
242	#135	C₂³×C₇	1	16	yes	—
243	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
244	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
245	C₂×D₈	C₂×C₄×C₇	1	4	yes	complemented
246	#131	—	2	32	no	—
247	#131	—	2	16	no	—
248	#131	C₂³×C₇	1	32	yes	complemented
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	4	no	—
251	C₂×M₁₆	—	2	32	no	—
252	C₂×M₁₆	—	2	8	no	—
253	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
254	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
255	C₂×M₁₆	C₇×D₄	1	4	yes	—
256	C₂×M₁₆	C₇×D₄	1	4	yes	—
257	C₂×M₁₆	C₂³×C₇	1	4	yes	—
258	C₂×M₁₆	C₂³×C₇	1	8	yes	—
259	C₂×M₁₆	C₂³×C₇	1	4	yes	—
260	C₂×M₁₆	C₂³×C₇	1	4	yes	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	8	no	—
263	C₂²×C₈	C₂³×C₇	1	2	yes	—
264	C₂²×C₈	C₂³×C₇	1	2	yes	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₇	1	4	yes	—
270	#108	C₂³×C₇	1	16	yes	complemented
271	#104	C₂³×C₇	1	16	yes	complemented
272	#104	C₂³×C₇	1	16	yes	complemented
273	#97	C₂³×C₇	1	8	yes	complemented
274	C₄×C₈	C₂³×C₇	1	8	yes	complemented
275	C₂²×C₇	—	2	2	no	—
276	C₂²×C₇	—	2	4	no	—
277	C₂²×C₇	—	2	8	no	—
278	C₂²×C₇	—	4	2	no	—
279	C₂²×C₇	—	4	2	no	—
280	C₂²×C₇	—	4	8	no	—
281	C₂²×C₇	—	8	8	no	—
282	C₂²×C₇	C₂×C₄×D₄	1	4	yes	—
283	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
284	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
286	C₄×C₇	—	2	4	no	—
287	C₄×C₇	—	2	8	no	—
288	C₄×C₇	—	4	2	no	—
289	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
290	C₄×C₇	C₂×C₄×D₄	1	4	yes	—
291	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
292	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
293	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
294	C₂⁴	—	2	2	no	—
295	C₂⁴	C₇×#41	1	1	yes	characteristic
296	#41	—	2	8	no	—
297	#41	—	2	8	no	—
298	#41	—	2	8	no	—
299	#41	—	2	8	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	8	no	—
303	#41	C₂²×C₄×C₇	1	8	yes	—
304	#41	C₂²×C₄×C₇	1	16	yes	—
305	#41	C₂⁴×C₇	1	8	yes	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
309	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
317	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
328	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
329	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
330	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
331	C₂²×C₄	C₇×#41	1	1	yes	characteristic
332	C₂²×C₄	C₇×#41	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
335	Q₁₆	C₂²×C₄×C₇	1	16	yes	complemented
336	SD₁₆	C₂²×C₄×C₇	1	32	yes	complemented
337	D₈	C₂²×C₄×C₇	1	16	yes	complemented
338	M₁₆	—	2	8	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	32	no	—
341	M₁₆	C₂²×C₄×C₇	1	16	yes	—
342	M₁₆	C₂×C₇×D₄	1	16	yes	—
343	M₁₆	C₂⁴×C₇	1	8	yes	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	8	no	—
346	C₂×C₈	—	2	32	no	—
347	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
348	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
349	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
350	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
351	C₂×C₈	C₂⁴×C₇	1	4	yes	—
352	C₂×C₈	C₂⁴×C₇	1	4	yes	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	4	no	—
355	C₄²	—	2	1	no	—
356	C₄²	C₂⁴×C₇	1	2	yes	—
357	C₄²	C₂⁴×C₇	1	2	yes	—
358	C₂×C₇	—	2	1	no	—
359	C₂×C₇	—	2	4	no	—
360	C₂×C₇	—	2	1	no	—
361	C₂×C₇	—	4	8	no	—
362	C₂×C₇	#2956	1	2	yes	direct product factor
363	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
364	C₂³	—	2	4	no	—
365	C₂³	—	2	8	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	8	4	no	—
368	C₂³	C₄×C₇×D₄	1	2	yes	—
369	C₂³	C₄×C₇×D₄	1	2	yes	—
370	C₂³	C₂×C₇×#41	1	1	yes	characteristic
371	C₂³	C₂×C₇×#41	1	2	yes	—
372	Q₈	—	2	8	no	—
373	Q₈	—	2	4	no	—
374	Q₈	C₂³×C₄×C₇	1	8	yes	—
375	D₄	—	2	8	no	—
376	D₄	—	2	16	no	—
377	D₄	—	2	8	no	—
378	D₄	—	2	8	no	—
379	D₄	—	2	4	no	—
380	D₄	C₂³×C₄×C₇	1	8	yes	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	16	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
392	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
393	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
394	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
395	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
396	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
397	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
398	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
400	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
402	C₂×C₄	C₂×C₇×#41	1	2	yes	—
403	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
404	C₈	—	2	8	no	—
405	C₈	C₂³×C₄×C₇	1	8	yes	—
406	C₈	C₂²×C₇×D₄	1	8	yes	—
407	C₇	C₂×#2956	1	1	yes	characteristic, direct product factor, Sylow
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	8	no	—
414	C₂²	—	8	8	no	—
415	C₂²	C₂×C₄×C₇×D₄	1	4	yes	—
416	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
417	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
418	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
419	C₄	—	2	4	no	—
420	C₄	—	2	8	no	—
421	C₄	—	4	2	no	—
422	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
423	C₄	C₂×C₄×C₇×D₄	1	4	yes	—
424	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
425	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
426	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	1	no	—
430	C₂	—	4	8	no	—
431	C₂	C₇×#2956	1	2	yes	direct product factor
432	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×C₇×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₇×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#568	C₂	semidirect
3. C₇×#2956	C₂	direct (N × H)
4. C₂×C₇×#444	C₂	semidirect
5. C₂×C₇×#443	C₂	semidirect
6. C₂×C₇×#430	C₂	semidirect
7. C₂²×C₇×#104	C₂	semidirect
8. C₂×C₄×C₇×M₁₆	C₂	semidirect
10. C₇×#575	C₄	semidirect
12. C₂×C₇×#137	C₄	semidirect
13. C₂×C₇×AGL(1,ℤ/8)	C₄	semidirect
16. C₇×#568	C₂²	semidirect
18. C₂×C₇×#131	C₂²	semidirect
24. C₇×#444	C₂²	semidirect
25. C₇×#443	C₂²	semidirect
26. C₇×#430	C₂²	semidirect
27. C₂×C₇×#108	C₂²	semidirect
28. C₂×C₇×#104	C₂²	semidirect
29. C₂×C₇×#104	C₂²	semidirect
30. C₂×C₇×#104	C₂²	semidirect
31. C₄×C₇×M₁₆	C₂²	semidirect
32. C₂×C₇×#97	C₂²	semidirect
33. C₂×C₄×C₇×C₈	C₂²	semidirect
34. C₂×#2956	C₇	direct (N × H)
49. C₇×#137	C₂×C₄	semidirect
50. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
51. C₇×#135	C₂×C₄	semidirect
53. C₂×C₇×Q₁₆	C₂×C₄	semidirect
54. C₂×C₇×SD₁₆	C₂×C₄	semidirect
55. C₂×C₇×D₈	C₂×C₄	semidirect
58. C₇×#131	C₂³	semidirect
80. C₇×#108	C₂³	semidirect
81. C₇×#104	C₂³	semidirect
82. C₇×#104	C₂³	semidirect
83. C₇×#97	C₂³	semidirect
84. C₄×C₇×C₈	C₂³	semidirect
86. C₂×#568	C₂×C₇	semidirect
87. #2956	C₂×C₇	direct (N × H)
88. C₂×#444	C₂×C₇	semidirect
89. C₂×#443	C₂×C₇	semidirect
90. C₂×#430	C₂×C₇	semidirect
91. C₂²×#104	C₂×C₇	semidirect
92. C₂×C₄×M₁₆	C₂×C₇	semidirect
134. C₇×Q₁₆	C₂²×C₄	semidirect
135. C₇×SD₁₆	C₂²×C₄	semidirect
136. C₇×D₈	C₂²×C₄	semidirect
158. #575	C₄×C₇	semidirect
160. C₂×#137	C₄×C₇	semidirect
161. C₂×AGL(1,ℤ/8)	C₄×C₇	semidirect
164. #568	C₂²×C₇	semidirect
166. C₂×#131	C₂²×C₇	semidirect
172. #444	C₂²×C₇	semidirect
173. #443	C₂²×C₇	semidirect
174. #430	C₂²×C₇	semidirect
175. C₂×#108	C₂²×C₇	semidirect
176. C₂×#104	C₂²×C₇	semidirect
177. C₂×#104	C₂²×C₇	semidirect
178. C₂×#104	C₂²×C₇	semidirect
179. C₄×M₁₆	C₂²×C₇	semidirect
180. C₂×#97	C₂²×C₇	semidirect
181. C₂×C₄×C₈	C₂²×C₇	semidirect
239. #137	C₂×C₄×C₇	semidirect
240. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
241. #135	C₂×C₄×C₇	semidirect
243. C₂×Q₁₆	C₂×C₄×C₇	semidirect
244. C₂×SD₁₆	C₂×C₄×C₇	semidirect
245. C₂×D₈	C₂×C₄×C₇	semidirect
248. #131	C₂³×C₇	semidirect
270. #108	C₂³×C₇	semidirect
271. #104	C₂³×C₇	semidirect
272. #104	C₂³×C₇	semidirect
273. #97	C₂³×C₇	semidirect
274. C₄×C₈	C₂³×C₇	semidirect
335. Q₁₆	C₂²×C₄×C₇	semidirect
336. SD₁₆	C₂²×C₄×C₇	semidirect
337. D₈	C₂²×C₄×C₇	semidirect
362. C₂×C₇	#2956	direct (N × H)
407. C₇	C₂×#2956	direct (N × H)
431. C₂	C₇×#2956	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×#575	2
C₂×C₇×#568	2
C₇×#2956	2
C₂×C₇×#444	2
C₂×C₇×#443	2
C₂×C₇×#430	2
C₂²×C₇×#104	2
C₂×C₄×C₇×M₁₆	2
C₂×#2956	7

Subgroups — C2×C7×#2956 #13237396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2956 #13237396