Subgroups — C₂×C₇×#3485 #13239990

Order 1792.

11686 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3485	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₇×#547	C₂	1	8	yes	maximal, complemented
5	C₂×C₇×#546	C₂	1	8	yes	maximal, complemented
6	C₂×C₇×#536	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#534	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
9	C₂²×C₇×#123	C₂	1	4	yes	maximal, complemented
10	C₂×C₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×H(5,𝔽₂)	—	2	16	no	—
12	C₂×C₇×H(5,𝔽₂)	C₂²	1	16	yes	complemented
13	C₂²×C₇×#41	—	2	16	no	—
14	C₂²×C₇×#41	C₂²	1	2	yes	—
15	C₂²×C₇×#41	C₂²	1	8	yes	complemented
16	C₂²×C₇×#41	C₂²	1	4	yes	complemented
17	C₂²×C₇×#41	C₂²	1	16	yes	complemented
18	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₇×D₄	C₂²	1	4	yes	—
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂³×C₇×D₄	C₂²	1	2	yes	complemented
22	C₂³×C₇×D₄	C₂²	1	4	yes	complemented
23	C₂⁴×C₄×C₇	C₂²	1	2	yes	complemented
24	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
25	C₇×#547	C₂²	1	128	yes	complemented
26	C₇×#546	C₂²	1	128	yes	complemented
27	C₇×#536	C₂²	1	32	yes	complemented
28	C₇×#534	C₂²	1	64	yes	complemented
29	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
30	C₂×C₇×#124	C₂²	1	4	yes	complemented
31	C₇×#525	C₂²	1	32	yes	complemented
32	C₂×C₇×#123	C₂²	1	4	yes	complemented
33	C₂×C₇×#123	C₂²	1	8	yes	complemented
34	C₂×C₇×#123	C₂²	1	16	yes	complemented
35	C₂×C₇×#123	C₂²	1	8	yes	complemented
36	C₂×C₇×#123	C₂²	1	64	yes	complemented
37	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
38	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
39	C₂×C₇×#121	C₂²	1	4	yes	complemented
40	C₂×C₇×#121	C₂²	1	16	yes	complemented
41	C₂×C₇×#120	C₂²	1	4	yes	complemented
42	C₂×C₇×#120	C₂²	1	8	yes	complemented
43	C₇×#518	C₂²	1	16	yes	complemented
44	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
45	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
46	C₂×C₇×#117	C₂²	1	2	yes	complemented
47	C₂²×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
48	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
49	C₂²×C₇×C₂²⋊C₄	C₂²	1	8	yes	complemented
50	C₂×#3485	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂⁵×C₇	C₂³	1	4	yes	—
52	C₂⁵×C₇	C₂³	1	1	yes	characteristic
53	C₂⁵×C₇	C₂³	1	2	yes	—
54	C₇×H(5,𝔽₂)	—	2	128	no	—
55	C₂×C₇×#41	—	2	64	no	—
56	C₂×C₇×#41	—	2	32	no	—
57	C₂×C₇×#41	—	2	128	no	—
58	C₂×C₇×#41	—	2	16	no	—
59	C₂×C₇×#41	C₂³	1	16	yes	—
60	C₂×C₇×#41	C₂³	1	64	yes	complemented
61	C₂×C₇×#41	C₂³	1	32	yes	complemented
62	C₂²×C₇×Q₈	—	2	8	no	—
63	C₂²×C₇×Q₈	C₂³	1	4	yes	—
64	C₂²×C₇×Q₈	C₂³	1	2	yes	—
65	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
66	C₂²×C₇×D₄	—	2	32	no	—
67	C₂²×C₇×D₄	—	2	16	no	—
68	C₂²×C₇×D₄	—	2	32	no	—
69	C₂²×C₇×D₄	D₄	1	16	yes	complemented
70	C₂²×C₇×D₄	C₂³	1	4	yes	—
71	C₂²×C₇×D₄	C₂³	1	8	yes	—
72	C₂²×C₇×D₄	C₂³	1	32	yes	—
73	C₂²×C₇×D₄	C₂³	1	2	yes	—
74	C₂²×C₇×D₄	C₂³	1	8	yes	—
75	C₂²×C₇×D₄	C₂³	1	8	yes	—
76	C₂²×C₇×D₄	C₂³	1	4	yes	—
77	C₂²×C₇×D₄	C₂³	1	8	yes	—
78	C₂²×C₇×D₄	C₂³	1	16	yes	complemented
79	C₂²×C₇×D₄	C₂³	1	32	yes	complemented
80	C₂³×C₄×C₇	—	2	16	no	—
81	C₂³×C₄×C₇	—	2	8	no	—
82	C₂³×C₄×C₇	C₂³	1	4	yes	—
83	C₂³×C₄×C₇	C₂³	1	2	yes	—
84	C₂³×C₄×C₇	C₂³	1	4	yes	—
85	C₂³×C₄×C₇	C₂³	1	8	yes	—
86	C₂³×C₄×C₇	C₂³	1	4	yes	—
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇	C₂³	1	8	yes	—
89	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇	C₂³	1	16	yes	complemented
91	C₂³×C₄×C₇	C₂³	1	8	yes	complemented
92	C₇×C₄⋊Q₈	C₂³	1	32	yes	complemented
93	C₇×#124	C₂³	1	32	yes	complemented
94	C₇×#123	C₂³	1	32	yes	complemented
95	C₇×#123	C₂³	1	64	yes	complemented
96	C₇×#123	C₂³	1	128	yes	complemented
97	C₇×#123	C₂³	1	64	yes	complemented
98	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
99	C₇×C₂²⋊Q₈	C₂³	1	64	yes	complemented
100	C₇×#121	C₂³	1	32	yes	complemented
101	C₇×#121	C₂³	1	128	yes	complemented
102	C₇×#120	C₂³	1	32	yes	complemented
103	C₇×#120	C₂³	1	64	yes	complemented
104	C₄×C₇×D₄	C₂³	1	64	yes	complemented
105	C₄×C₇×D₄	C₂³	1	64	yes	complemented
106	C₇×#117	C₂³	1	16	yes	complemented
107	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	64	yes	complemented
111	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
113	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
114	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
115	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
116	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
117	C₂×C₇×C₂²⋊C₄	C₂³	1	64	yes	complemented
118	C₂×C₄²×C₇	C₂³	1	4	yes	—
119	C₂²×H(5,𝔽₂)	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂³×#41	C₂×C₇	1	1	yes	characteristic, complemented
121	#3485	C₂×C₇	1	32	yes	direct product factor
122	C₂×#547	C₂×C₇	1	8	yes	complemented
123	C₂×#546	C₂×C₇	1	8	yes	complemented
124	C₂×#536	C₂×C₇	1	2	yes	complemented
125	C₂×#534	C₂×C₇	1	4	yes	complemented
126	C₂×#525	C₂×C₇	1	2	yes	complemented
127	C₂²×#123	C₂×C₇	1	4	yes	complemented
128	C₂×#518	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂⁴×C₇	—	2	4	no	—
130	C₂⁴×C₇	—	2	16	no	—
131	C₂⁴×C₇	—	4	8	no	—
132	C₂⁴×C₇	—	4	4	no	—
133	C₂⁴×C₇	—	4	16	no	—
134	C₂⁴×C₇	C₂×D₄	1	16	yes	—
135	C₂⁴×C₇	C₂⁴	1	4	yes	—
136	C₂⁴×C₇	C₂⁴	1	2	yes	—
137	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
138	C₂⁴×C₇	C₂⁴	1	4	yes	—
139	C₂⁴×C₇	C₂⁴	1	16	yes	—
140	C₂⁴×C₇	C₂⁴	1	4	yes	—
141	C₂⁴×C₇	C₂⁴	1	8	yes	—
142	C₇×#41	—	2	256	no	—
143	C₇×#41	—	2	128	no	—
144	C₇×#41	—	2	64	no	—
145	C₂×C₇×Q₈	—	2	16	no	—
146	C₂×C₇×Q₈	—	2	32	no	—
147	C₂×C₇×Q₈	—	2	8	no	—
148	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
149	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
150	C₂×C₇×D₄	—	2	16	no	—
151	C₂×C₇×D₄	—	2	32	no	—
152	C₂×C₇×D₄	—	2	32	no	—
153	C₂×C₇×D₄	—	2	128	no	—
154	C₂×C₇×D₄	—	2	64	no	—
155	C₂×C₇×D₄	—	2	128	no	—
156	C₂×C₇×D₄	—	2	8	no	—
157	C₂×C₇×D₄	—	4	16	no	—
158	C₂×C₇×D₄	C₂×D₄	1	32	yes	—
159	C₂×C₇×D₄	C₂×D₄	1	64	yes	complemented
160	C₂×C₇×D₄	C₂⁴	1	32	yes	—
161	C₂×C₇×D₄	C₂⁴	1	16	yes	—
162	C₂×C₇×D₄	C₂⁴	1	32	yes	—
163	C₂×C₇×D₄	C₂⁴	1	8	yes	—
164	C₂×C₇×D₄	C₂⁴	1	32	yes	—
165	C₂×C₇×D₄	C₂⁴	1	16	yes	—
166	C₂²×C₄×C₇	—	2	4	no	—
167	C₂²×C₄×C₇	—	2	8	no	—
168	C₂²×C₄×C₇	—	2	32	no	—
169	C₂²×C₄×C₇	—	2	64	no	—
170	C₂²×C₄×C₇	—	2	16	no	—
171	C₂²×C₄×C₇	—	2	16	no	—
172	C₂²×C₄×C₇	—	2	32	no	—
173	C₂²×C₄×C₇	—	2	16	no	—
174	C₂²×C₄×C₇	—	4	16	no	—
175	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
176	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
177	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
178	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
179	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
180	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
182	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
183	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
187	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
189	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
190	C₇×C₄⋊C₄	C₂⁴	1	64	yes	—
191	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
192	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
193	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
194	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
195	C₇×C₂²⋊C₄	C₂⁴	1	64	yes	—
196	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
197	C₄²×C₇	C₂⁴	1	16	yes	—
198	C₂×H(5,𝔽₂)	—	2	16	no	—
199	C₂×H(5,𝔽₂)	C₂²×C₇	1	16	yes	complemented
200	C₂²×#41	—	2	16	no	—
201	C₂²×#41	C₂²×C₇	1	2	yes	—
202	C₂²×#41	C₂²×C₇	1	8	yes	complemented
203	C₂²×#41	C₂²×C₇	1	4	yes	complemented
204	C₂²×#41	C₂²×C₇	1	16	yes	complemented
205	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
206	C₂³×D₄	C₂²×C₇	1	4	yes	—
207	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
208	C₂³×D₄	C₂²×C₇	1	2	yes	complemented
209	C₂³×D₄	C₂²×C₇	1	4	yes	complemented
210	C₂⁴×C₄	C₂²×C₇	1	2	yes	complemented
211	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
212	#547	C₂²×C₇	1	128	yes	complemented
213	#546	C₂²×C₇	1	128	yes	complemented
214	#536	C₂²×C₇	1	32	yes	complemented
215	#534	C₂²×C₇	1	64	yes	complemented
216	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	complemented
217	C₂×#124	C₂²×C₇	1	4	yes	complemented
218	#525	C₂²×C₇	1	32	yes	complemented
219	C₂×#123	C₂²×C₇	1	4	yes	complemented
220	C₂×#123	C₂²×C₇	1	8	yes	complemented
221	C₂×#123	C₂²×C₇	1	16	yes	complemented
222	C₂×#123	C₂²×C₇	1	8	yes	complemented
223	C₂×#123	C₂²×C₇	1	64	yes	complemented
224	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
225	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
226	C₂×#121	C₂²×C₇	1	4	yes	complemented
227	C₂×#121	C₂²×C₇	1	16	yes	complemented
228	C₂×#120	C₂²×C₇	1	4	yes	complemented
229	C₂×#120	C₂²×C₇	1	8	yes	complemented
230	#518	C₂²×C₇	1	16	yes	complemented
231	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
232	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
233	C₂×#117	C₂²×C₇	1	2	yes	complemented
234	C₂²×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
235	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
236	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	complemented
237	C₂³×C₇	—	2	16	no	—
238	C₂³×C₇	—	2	4	no	—
239	C₂³×C₇	—	2	8	no	—
240	C₂³×C₇	—	2	4	no	—
241	C₂³×C₇	—	2	8	no	—
242	C₂³×C₇	—	2	8	no	—
243	C₂³×C₇	—	2	16	no	—
244	C₂³×C₇	—	2	32	no	—
245	C₂³×C₇	—	4	32	no	—
246	C₂³×C₇	—	4	16	no	—
247	C₂³×C₇	—	4	8	no	—
248	C₂³×C₇	—	4	32	no	—
249	C₂³×C₇	—	4	16	no	—
250	C₂³×C₇	—	8	32	no	—
251	C₂³×C₇	C₂²×D₄	1	4	yes	—
252	C₂³×C₇	C₂²×D₄	1	16	yes	—
253	C₂³×C₇	C₂²×D₄	1	32	yes	—
254	C₂³×C₇	C₂⁵	1	8	yes	—
255	C₂³×C₇	C₂⁵	1	4	yes	—
256	C₂³×C₇	C₂⁵	1	2	yes	—
257	C₂³×C₇	C₂⁵	1	8	yes	—
258	C₂³×C₇	C₂⁵	1	1	yes	characteristic
259	C₇×Q₈	—	2	32	no	—
260	C₇×Q₈	—	2	16	no	—
261	C₇×D₄	—	2	32	no	—
262	C₇×D₄	—	2	64	no	—
263	C₇×D₄	—	2	64	no	—
264	C₇×D₄	—	2	16	no	—
265	C₇×D₄	—	4	32	no	—
266	C₇×D₄	C₂²×D₄	1	64	yes	—
267	C₂×C₄×C₇	—	2	8	no	—
268	C₂×C₄×C₇	—	2	4	no	—
269	C₂×C₄×C₇	—	2	8	no	—
270	C₂×C₄×C₇	—	2	16	no	—
271	C₂×C₄×C₇	—	2	8	no	—
272	C₂×C₄×C₇	—	2	64	no	—
273	C₂×C₄×C₇	—	2	32	no	—
274	C₂×C₄×C₇	—	2	16	no	—
275	C₂×C₄×C₇	—	2	32	no	—
276	C₂×C₄×C₇	—	2	32	no	—
277	C₂×C₄×C₇	—	4	32	no	—
278	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
279	C₂×C₄×C₇	C₂²×D₄	1	16	yes	—
280	C₂×C₄×C₇	C₂⁵	1	16	yes	—
281	C₂×C₄×C₇	C₂⁵	1	4	yes	—
282	C₂×C₄×C₇	C₂⁵	1	8	yes	—
283	C₂×C₄×C₇	C₂⁵	1	8	yes	—
284	C₂×C₄×C₇	C₂⁵	1	4	yes	—
285	C₂⁵	C₂³×C₇	1	4	yes	—
286	C₂⁵	C₂³×C₇	1	1	yes	characteristic
287	C₂⁵	C₂³×C₇	1	2	yes	—
288	H(5,𝔽₂)	—	2	128	no	—
289	C₂×#41	—	2	64	no	—
290	C₂×#41	—	2	32	no	—
291	C₂×#41	—	2	128	no	—
292	C₂×#41	—	2	16	no	—
293	C₂×#41	C₂³×C₇	1	16	yes	—
294	C₂×#41	C₂³×C₇	1	64	yes	complemented
295	C₂×#41	C₂³×C₇	1	32	yes	complemented
296	C₂²×Q₈	—	2	8	no	—
297	C₂²×Q₈	C₂³×C₇	1	4	yes	—
298	C₂²×Q₈	C₂³×C₇	1	2	yes	—
299	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
300	C₂²×D₄	—	2	32	no	—
301	C₂²×D₄	—	2	16	no	—
302	C₂²×D₄	—	2	32	no	—
303	C₂²×D₄	C₇×D₄	1	16	yes	complemented
304	C₂²×D₄	C₂³×C₇	1	8	yes	—
305	C₂²×D₄	C₂³×C₇	1	4	yes	—
306	C₂²×D₄	C₂³×C₇	1	8	yes	—
307	C₂²×D₄	C₂³×C₇	1	2	yes	—
308	C₂²×D₄	C₂³×C₇	1	32	yes	—
309	C₂²×D₄	C₂³×C₇	1	8	yes	—
310	C₂²×D₄	C₂³×C₇	1	4	yes	—
311	C₂²×D₄	C₂³×C₇	1	8	yes	—
312	C₂²×D₄	C₂³×C₇	1	16	yes	complemented
313	C₂²×D₄	C₂³×C₇	1	32	yes	complemented
314	C₂³×C₄	—	2	16	no	—
315	C₂³×C₄	—	2	8	no	—
316	C₂³×C₄	C₂³×C₇	1	8	yes	—
317	C₂³×C₄	C₂³×C₇	1	4	yes	—
318	C₂³×C₄	C₂³×C₇	1	4	yes	—
319	C₂³×C₄	C₂³×C₇	1	4	yes	—
320	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₇	1	2	yes	—
322	C₂³×C₄	C₂³×C₇	1	8	yes	—
323	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₇	1	16	yes	complemented
325	C₂³×C₄	C₂³×C₇	1	8	yes	complemented
326	C₄⋊Q₈	C₂³×C₇	1	32	yes	complemented
327	#124	C₂³×C₇	1	32	yes	complemented
328	#123	C₂³×C₇	1	32	yes	complemented
329	#123	C₂³×C₇	1	64	yes	complemented
330	#123	C₂³×C₇	1	128	yes	complemented
331	#123	C₂³×C₇	1	64	yes	complemented
332	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
333	C₂²⋊Q₈	C₂³×C₇	1	64	yes	complemented
334	#121	C₂³×C₇	1	32	yes	complemented
335	#121	C₂³×C₇	1	128	yes	complemented
336	#120	C₂³×C₇	1	32	yes	complemented
337	#120	C₂³×C₇	1	64	yes	complemented
338	C₄×D₄	C₂³×C₇	1	64	yes	complemented
339	C₄×D₄	C₂³×C₇	1	64	yes	complemented
340	#117	C₂³×C₇	1	16	yes	complemented
341	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
342	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
343	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₇	1	64	yes	complemented
345	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
351	C₂×C₂²⋊C₄	C₂³×C₇	1	64	yes	complemented
352	C₂×C₄²	C₂³×C₇	1	4	yes	—
353	C₂²×C₇	—	2	16	no	—
354	C₂²×C₇	—	2	4	no	—
355	C₂²×C₇	—	2	8	no	—
356	C₂²×C₇	—	2	32	no	—
357	C₂²×C₇	—	2	4	no	—
358	C₂²×C₇	—	2	8	no	—
359	C₂²×C₇	—	2	8	no	—
360	C₂²×C₇	—	2	16	no	—
361	C₂²×C₇	—	4	32	no	—
362	C₂²×C₇	—	4	16	no	—
363	C₂²×C₇	—	4	8	no	—
364	C₂²×C₇	—	4	16	no	—
365	C₂²×C₇	—	8	32	no	—
366	C₂²×C₇	C₂³×D₄	1	4	yes	—
367	C₂²×C₇	C₂³×D₄	1	16	yes	—
368	C₂²×C₇	C₂³×D₄	1	2	yes	—
369	C₂²×C₇	#585	1	4	yes	—
370	C₂²×C₇	C₂⁶	1	1	yes	characteristic
371	C₄×C₇	—	2	4	no	—
372	C₄×C₇	—	2	8	no	—
373	C₄×C₇	—	2	8	no	—
374	C₄×C₇	—	2	16	no	—
375	C₄×C₇	C₂³×D₄	1	8	yes	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	16	no	—
378	C₂⁴	—	4	8	no	—
379	C₂⁴	—	4	4	no	—
380	C₂⁴	—	4	16	no	—
381	C₂⁴	C₂×C₇×D₄	1	16	yes	—
382	C₂⁴	C₂⁴×C₇	1	4	yes	—
383	C₂⁴	C₂⁴×C₇	1	2	yes	—
384	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
385	C₂⁴	C₂⁴×C₇	1	4	yes	—
386	C₂⁴	C₂⁴×C₇	1	16	yes	—
387	C₂⁴	C₂⁴×C₇	1	4	yes	—
388	C₂⁴	C₂⁴×C₇	1	8	yes	—
389	#41	—	2	256	no	—
390	#41	—	2	128	no	—
391	#41	—	2	64	no	—
392	C₂×Q₈	—	2	16	no	—
393	C₂×Q₈	—	2	32	no	—
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
396	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
397	C₂×D₄	—	2	16	no	—
398	C₂×D₄	—	2	32	no	—
399	C₂×D₄	—	2	32	no	—
400	C₂×D₄	—	2	128	no	—
401	C₂×D₄	—	2	64	no	—
402	C₂×D₄	—	2	128	no	—
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	4	16	no	—
405	C₂×D₄	C₂×C₇×D₄	1	32	yes	—
406	C₂×D₄	C₂×C₇×D₄	1	64	yes	complemented
407	C₂×D₄	C₂⁴×C₇	1	32	yes	—
408	C₂×D₄	C₂⁴×C₇	1	16	yes	—
409	C₂×D₄	C₂⁴×C₇	1	32	yes	—
410	C₂×D₄	C₂⁴×C₇	1	8	yes	—
411	C₂×D₄	C₂⁴×C₇	1	32	yes	—
412	C₂×D₄	C₂⁴×C₇	1	16	yes	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	32	no	—
416	C₂²×C₄	—	2	64	no	—
417	C₂²×C₄	—	2	16	no	—
418	C₂²×C₄	—	2	16	no	—
419	C₂²×C₄	—	2	32	no	—
420	C₂²×C₄	—	2	16	no	—
421	C₂²×C₄	—	4	16	no	—
422	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
423	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
424	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
428	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
429	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
430	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
431	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
433	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
434	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
436	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
437	C₄⋊C₄	C₂⁴×C₇	1	64	yes	—
438	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
439	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
440	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
441	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
442	C₂²⋊C₄	C₂⁴×C₇	1	64	yes	—
443	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
444	C₄²	C₂⁴×C₇	1	16	yes	—
445	C₂×C₇	—	2	4	no	—
446	C₂×C₇	—	2	16	no	—
447	C₂×C₇	—	4	4	no	—
448	C₂×C₇	—	4	8	no	—
449	C₂×C₇	#3485	1	4	yes	direct product factor
450	C₂×C₇	C₂⁴×D₄	1	1	yes	characteristic
451	C₂×C₇	C₂×#585	1	2	yes	—
452	C₂³	—	2	16	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	8	no	—
457	C₂³	—	2	8	no	—
458	C₂³	—	2	16	no	—
459	C₂³	—	2	32	no	—
460	C₂³	—	4	32	no	—
461	C₂³	—	4	16	no	—
462	C₂³	—	4	8	no	—
463	C₂³	—	4	32	no	—
464	C₂³	—	4	16	no	—
465	C₂³	—	8	32	no	—
466	C₂³	C₂²×C₇×D₄	1	4	yes	—
467	C₂³	C₂²×C₇×D₄	1	16	yes	—
468	C₂³	C₂²×C₇×D₄	1	32	yes	—
469	C₂³	C₂⁵×C₇	1	8	yes	—
470	C₂³	C₂⁵×C₇	1	4	yes	—
471	C₂³	C₂⁵×C₇	1	2	yes	—
472	C₂³	C₂⁵×C₇	1	8	yes	—
473	C₂³	C₂⁵×C₇	1	1	yes	characteristic
474	Q₈	—	2	32	no	—
475	Q₈	—	2	16	no	—
476	D₄	—	2	32	no	—
477	D₄	—	2	64	no	—
478	D₄	—	2	64	no	—
479	D₄	—	2	16	no	—
480	D₄	—	4	32	no	—
481	D₄	C₂²×C₇×D₄	1	64	yes	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	16	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	64	no	—
488	C₂×C₄	—	2	32	no	—
489	C₂×C₄	—	2	16	no	—
490	C₂×C₄	—	2	32	no	—
491	C₂×C₄	—	2	32	no	—
492	C₂×C₄	—	4	32	no	—
493	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
494	C₂×C₄	C₂²×C₇×D₄	1	16	yes	—
495	C₂×C₄	C₂⁵×C₇	1	16	yes	—
496	C₂×C₄	C₂⁵×C₇	1	4	yes	—
497	C₂×C₄	C₂⁵×C₇	1	8	yes	—
498	C₂×C₄	C₂⁵×C₇	1	8	yes	—
499	C₂×C₄	C₂⁵×C₇	1	4	yes	—
500	C₇	C₂×#3485	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²	—	2	16	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	32	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	2	16	no	—
509	C₂²	—	4	32	no	—
510	C₂²	—	4	16	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	16	no	—
513	C₂²	—	8	32	no	—
514	C₂²	C₂³×C₇×D₄	1	4	yes	—
515	C₂²	C₂³×C₇×D₄	1	16	yes	—
516	C₂²	C₂³×C₇×D₄	1	2	yes	—
517	C₂²	C₇×#585	1	4	yes	—
518	C₂²	C₂⁶×C₇	1	1	yes	characteristic
519	C₄	—	2	4	no	—
520	C₄	—	2	8	no	—
521	C₄	—	2	8	no	—
522	C₄	—	2	16	no	—
523	C₄	C₂³×C₇×D₄	1	8	yes	—
524	C₂	—	2	4	no	—
525	C₂	—	2	16	no	—
526	C₂	—	4	4	no	—
527	C₂	—	4	8	no	—
528	C₂	C₇×#3485	1	4	yes	direct product factor
529	C₂	C₂⁴×C₇×D₄	1	1	yes	characteristic
530	C₂	C₂×C₇×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×H(5,𝔽₂)	C₂	semidirect
2. C₂³×C₇×#41	C₂	semidirect
3. C₇×#3485	C₂	direct (N × H)
4. C₂×C₇×#547	C₂	semidirect
5. C₂×C₇×#546	C₂	semidirect
6. C₂×C₇×#536	C₂	semidirect
7. C₂×C₇×#534	C₂	semidirect
8. C₂×C₇×#525	C₂	semidirect
9. C₂²×C₇×#123	C₂	semidirect
10. C₂×C₇×#518	C₂	semidirect
12. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
15. C₂²×C₇×#41	C₂²	semidirect
16. C₂²×C₇×#41	C₂²	semidirect
17. C₂²×C₇×#41	C₂²	semidirect
18. C₂³×C₇×Q₈	C₂²	semidirect
21. C₂³×C₇×D₄	C₂²	semidirect
22. C₂³×C₇×D₄	C₂²	semidirect
23. C₂⁴×C₄×C₇	C₂²	semidirect
24. C₂⁴×C₄×C₇	C₂²	semidirect
25. C₇×#547	C₂²	semidirect
26. C₇×#546	C₂²	semidirect
27. C₇×#536	C₂²	semidirect
28. C₇×#534	C₂²	semidirect
29. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₇×#124	C₂²	semidirect
31. C₇×#525	C₂²	semidirect
32. C₂×C₇×#123	C₂²	semidirect
33. C₂×C₇×#123	C₂²	semidirect
34. C₂×C₇×#123	C₂²	semidirect
35. C₂×C₇×#123	C₂²	semidirect
36. C₂×C₇×#123	C₂²	semidirect
37. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₇×#121	C₂²	semidirect
40. C₂×C₇×#121	C₂²	semidirect
41. C₂×C₇×#120	C₂²	semidirect
42. C₂×C₇×#120	C₂²	semidirect
43. C₇×#518	C₂²	semidirect
44. C₂×C₄×C₇×D₄	C₂²	semidirect
45. C₂×C₄×C₇×D₄	C₂²	semidirect
46. C₂×C₇×#117	C₂²	semidirect
47. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
48. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
49. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
50. C₂×#3485	C₇	direct (N × H)
60. C₂×C₇×#41	C₂³	semidirect
61. C₂×C₇×#41	C₂³	semidirect
65. C₂²×C₇×Q₈	C₂³	semidirect
69. C₂²×C₇×D₄	D₄	semidirect
78. C₂²×C₇×D₄	C₂³	semidirect
79. C₂²×C₇×D₄	C₂³	semidirect
90. C₂³×C₄×C₇	C₂³	semidirect
91. C₂³×C₄×C₇	C₂³	semidirect
92. C₇×C₄⋊Q₈	C₂³	semidirect
93. C₇×#124	C₂³	semidirect
94. C₇×#123	C₂³	semidirect
95. C₇×#123	C₂³	semidirect
96. C₇×#123	C₂³	semidirect
97. C₇×#123	C₂³	semidirect
98. C₇×C₂²⋊Q₈	C₂³	semidirect
99. C₇×C₂²⋊Q₈	C₂³	semidirect
100. C₇×#121	C₂³	semidirect
101. C₇×#121	C₂³	semidirect
102. C₇×#120	C₂³	semidirect
103. C₇×#120	C₂³	semidirect
104. C₄×C₇×D₄	C₂³	semidirect
105. C₄×C₇×D₄	C₂³	semidirect
106. C₇×#117	C₂³	semidirect
110. C₂×C₇×C₄⋊C₄	C₂³	semidirect
116. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
117. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
119. C₂²×H(5,𝔽₂)	C₂×C₇	semidirect
120. C₂³×#41	C₂×C₇	semidirect
121. #3485	C₂×C₇	direct (N × H)
122. C₂×#547	C₂×C₇	semidirect
123. C₂×#546	C₂×C₇	semidirect
124. C₂×#536	C₂×C₇	semidirect
125. C₂×#534	C₂×C₇	semidirect
126. C₂×#525	C₂×C₇	semidirect
127. C₂²×#123	C₂×C₇	semidirect
128. C₂×#518	C₂×C₇	semidirect
159. C₂×C₇×D₄	C₂×D₄	semidirect
199. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
202. C₂²×#41	C₂²×C₇	semidirect
203. C₂²×#41	C₂²×C₇	semidirect
204. C₂²×#41	C₂²×C₇	semidirect
205. C₂³×Q₈	C₂²×C₇	semidirect
208. C₂³×D₄	C₂²×C₇	semidirect
209. C₂³×D₄	C₂²×C₇	semidirect
210. C₂⁴×C₄	C₂²×C₇	semidirect
211. C₂⁴×C₄	C₂²×C₇	semidirect
212. #547	C₂²×C₇	semidirect
213. #546	C₂²×C₇	semidirect
214. #536	C₂²×C₇	semidirect
215. #534	C₂²×C₇	semidirect
216. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
217. C₂×#124	C₂²×C₇	semidirect
218. #525	C₂²×C₇	semidirect
219. C₂×#123	C₂²×C₇	semidirect
220. C₂×#123	C₂²×C₇	semidirect
221. C₂×#123	C₂²×C₇	semidirect
222. C₂×#123	C₂²×C₇	semidirect
223. C₂×#123	C₂²×C₇	semidirect
224. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
225. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
226. C₂×#121	C₂²×C₇	semidirect
227. C₂×#121	C₂²×C₇	semidirect
228. C₂×#120	C₂²×C₇	semidirect
229. C₂×#120	C₂²×C₇	semidirect
230. #518	C₂²×C₇	semidirect
231. C₂×C₄×D₄	C₂²×C₇	semidirect
232. C₂×C₄×D₄	C₂²×C₇	semidirect
233. C₂×#117	C₂²×C₇	semidirect
234. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
235. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
236. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
294. C₂×#41	C₂³×C₇	semidirect
295. C₂×#41	C₂³×C₇	semidirect
299. C₂²×Q₈	C₂³×C₇	semidirect
303. C₂²×D₄	C₇×D₄	semidirect
312. C₂²×D₄	C₂³×C₇	semidirect
313. C₂²×D₄	C₂³×C₇	semidirect
324. C₂³×C₄	C₂³×C₇	semidirect
325. C₂³×C₄	C₂³×C₇	semidirect
326. C₄⋊Q₈	C₂³×C₇	semidirect
327. #124	C₂³×C₇	semidirect
328. #123	C₂³×C₇	semidirect
329. #123	C₂³×C₇	semidirect
330. #123	C₂³×C₇	semidirect
331. #123	C₂³×C₇	semidirect
332. C₂²⋊Q₈	C₂³×C₇	semidirect
333. C₂²⋊Q₈	C₂³×C₇	semidirect
334. #121	C₂³×C₇	semidirect
335. #121	C₂³×C₇	semidirect
336. #120	C₂³×C₇	semidirect
337. #120	C₂³×C₇	semidirect
338. C₄×D₄	C₂³×C₇	semidirect
339. C₄×D₄	C₂³×C₇	semidirect
340. #117	C₂³×C₇	semidirect
344. C₂×C₄⋊C₄	C₂³×C₇	semidirect
350. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
351. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
406. C₂×D₄	C₂×C₇×D₄	semidirect
449. C₂×C₇	#3485	direct (N × H)
500. C₇	C₂×#3485	direct (N × H)
528. C₂	C₇×#3485	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×H(5,𝔽₂)	2
C₂³×C₇×#41	2
C₇×#3485	2
C₂×C₇×#547	2
C₂×C₇×#546	2
C₂×C₇×#536	2
C₂×C₇×#534	2
C₂×C₇×#525	2
C₂²×C₇×#123	2
C₂×C₇×#518	2
C₂×#3485	7

Subgroups — C2×C7×#3485 #13239990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3485 #13239990