Subgroups — C₂×C₇×#3493 #13239992

Order 1792.

7302 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3493	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#556	C₂	1	4	yes	maximal, complemented
3	C₂×C₇×#555	C₂	1	4	yes	maximal, complemented
4	C₂×C₇×#553	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#552	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#538	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×#537	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#529	C₂	1	4	yes	maximal, complemented
10	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#520	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
15	C₇×#556	C₂²	1	64	yes	complemented
16	C₇×#555	C₂²	1	64	yes	complemented
17	C₇×#553	C₂²	1	64	yes	complemented
18	C₇×#552	C₂²	1	64	yes	complemented
19	C₇×#544	C₂²	1	16	yes	complemented
20	C₇×#538	C₂²	1	64	yes	complemented
21	C₇×#537	C₂²	1	16	yes	complemented
22	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
23	C₇×#529	C₂²	1	64	yes	complemented
24	C₂×C₇×#126	C₂²	1	8	yes	—
25	C₂×C₇×#126	C₂²	1	8	yes	complemented
26	C₂×C₇×#125	C₂²	1	4	yes	complemented
27	C₂×C₇×#125	C₂²	1	4	yes	complemented
28	C₂×C₇×#124	C₂²	1	8	yes	—
29	C₂×C₇×#124	C₂²	1	4	yes	complemented
30	C₇×#525	C₂²	1	32	yes	complemented
31	C₂×C₇×#123	C₂²	1	4	yes	—
32	C₂×C₇×#123	C₂²	1	8	yes	—
33	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
37	C₂×C₇×#121	C₂²	1	2	yes	—
38	C₂×C₇×#121	C₂²	1	2	yes	—
39	C₂×C₇×#121	C₂²	1	4	yes	—
40	C₂×C₇×#121	C₂²	1	8	yes	—
41	C₂×C₇×#121	C₂²	1	4	yes	complemented
42	C₂×C₇×#120	C₂²	1	4	yes	—
43	C₇×#520	C₂²	1	32	yes	complemented
44	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
45	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
46	C₂×C₄×C₇×D₄	C₂²	1	8	yes	—
47	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
48	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
49	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
50	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
51	C₂×C₇×#117	C₂²	1	4	yes	—
52	C₂×C₇×#117	C₂²	1	4	yes	—
53	C₂×C₇×#117	C₂²	1	2	yes	—
54	C₂×C₇×#117	C₂²	1	16	yes	complemented
55	C₂×C₇×#117	C₂²	1	4	yes	complemented
56	C₂×C₇×#117	C₂²	1	8	yes	complemented
57	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	complemented
60	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
61	C₂²×C₄²×C₇	C₂²	1	2	yes	—
62	C₂×#3493	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂⁵×C₇	C₂³	1	1	yes	characteristic
64	C₂×C₇×#41	—	2	16	no	—
65	C₂×C₇×#41	C₂³	1	16	yes	—
66	C₂²×C₇×Q₈	C₂³	1	2	yes	—
67	C₂²×C₇×Q₈	C₂³	1	4	yes	—
68	C₂²×C₇×D₄	C₂³	1	4	yes	—
69	C₂²×C₇×D₄	C₂³	1	2	yes	—
70	C₂²×C₇×D₄	C₂³	1	4	yes	—
71	C₂²×C₇×D₄	C₂³	1	4	yes	—
72	C₂²×C₇×D₄	C₂³	1	4	yes	—
73	C₂³×C₄×C₇	—	2	8	no	—
74	C₂³×C₄×C₇	C₂³	1	4	yes	—
75	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₇	C₂³	1	2	yes	—
77	C₂³×C₄×C₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₇	C₂³	1	8	yes	—
79	C₂³×C₄×C₇	C₂³	1	2	yes	—
80	C₂³×C₄×C₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₇	C₂³	1	8	yes	—
82	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
83	C₇×C₄⋊Q₈	C₂³	1	32	yes	complemented
84	C₇×#126	C₂³	1	64	yes	—
85	C₇×#126	C₂³	1	64	yes	complemented
86	C₇×#125	C₂³	1	32	yes	complemented
87	C₇×#125	C₂³	1	32	yes	complemented
88	C₇×#124	C₂³	1	64	yes	—
89	C₇×#124	C₂³	1	32	yes	complemented
90	C₇×#123	C₂³	1	32	yes	—
91	C₇×#123	C₂³	1	64	yes	—
92	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
93	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
94	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
95	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
96	C₇×#121	C₂³	1	16	yes	—
97	C₇×#121	C₂³	1	16	yes	—
98	C₇×#121	C₂³	1	32	yes	—
99	C₇×#121	C₂³	1	64	yes	—
100	C₇×#121	C₂³	1	32	yes	complemented
101	C₇×#120	C₂³	1	32	yes	—
102	C₄×C₇×Q₈	C₂³	1	32	yes	complemented
103	C₄×C₇×Q₈	C₂³	1	32	yes	complemented
104	C₄×C₇×D₄	C₂³	1	64	yes	—
105	C₄×C₇×D₄	C₂³	1	32	yes	—
106	C₄×C₇×D₄	C₂³	1	32	yes	—
107	C₄×C₇×D₄	C₂³	1	32	yes	complemented
108	C₄×C₇×D₄	C₂³	1	32	yes	complemented
109	C₇×#117	C₂³	1	32	yes	—
110	C₇×#117	C₂³	1	32	yes	—
111	C₇×#117	C₂³	1	16	yes	—
112	C₇×#117	C₂³	1	32	yes	complemented
113	C₇×#117	C₂³	1	64	yes	complemented
114	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
117	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
118	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
120	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
123	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	complemented
127	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
129	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
132	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
133	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₄²×C₇	C₂³	1	4	yes	—
137	C₂×C₄²×C₇	C₂³	1	4	yes	—
138	C₂×C₄²×C₇	C₂³	1	16	yes	—
139	C₂×C₄²×C₇	C₂³	1	4	yes	—
140	C₂×C₄²×C₇	C₂³	1	8	yes	—
141	#3493	C₂×C₇	1	32	yes	direct product factor
142	C₂×#556	C₂×C₇	1	4	yes	complemented
143	C₂×#555	C₂×C₇	1	4	yes	complemented
144	C₂×#553	C₂×C₇	1	4	yes	complemented
145	C₂×#552	C₂×C₇	1	4	yes	complemented
146	C₂×#544	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#538	C₂×C₇	1	4	yes	complemented
148	C₂×#537	C₂×C₇	1	1	yes	characteristic, complemented
149	C₂×#529	C₂×C₇	1	4	yes	complemented
150	C₂×#525	C₂×C₇	1	2	yes	complemented
151	C₂×#520	C₂×C₇	1	2	yes	complemented
152	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
153	C₂⁴×C₇	—	2	4	no	—
154	C₂⁴×C₇	—	4	2	no	—
155	C₂⁴×C₇	—	4	2	no	—
156	C₂⁴×C₇	C₂⁴	1	2	yes	—
157	C₂⁴×C₇	C₂⁴	1	4	yes	—
158	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₇	C₂⁴	1	4	yes	—
160	C₇×#41	—	2	64	no	—
161	C₂×C₇×Q₈	—	2	8	no	—
162	C₂×C₇×Q₈	—	4	8	no	—
163	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
164	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
165	C₂×C₇×D₄	—	2	16	no	—
166	C₂×C₇×D₄	—	2	8	no	—
167	C₂×C₇×D₄	—	4	8	no	—
168	C₂×C₇×D₄	—	4	8	no	—
169	C₂×C₇×D₄	—	4	8	no	—
170	C₂×C₇×D₄	C₂⁴	1	16	yes	—
171	C₂×C₇×D₄	C₂⁴	1	8	yes	—
172	C₂×C₇×D₄	C₂⁴	1	16	yes	—
173	C₂×C₇×D₄	C₂⁴	1	16	yes	—
174	C₂×C₇×D₄	C₂⁴	1	16	yes	—
175	C₂²×C₄×C₇	—	2	4	no	—
176	C₂²×C₄×C₇	—	2	8	no	—
177	C₂²×C₄×C₇	—	2	8	no	—
178	C₂²×C₄×C₇	—	2	32	no	—
179	C₂²×C₄×C₇	—	2	16	no	—
180	C₂²×C₄×C₇	—	4	4	no	—
181	C₂²×C₄×C₇	—	4	16	no	—
182	C₂²×C₄×C₇	—	4	4	no	—
183	C₂²×C₄×C₇	#41	1	8	yes	—
184	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
186	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
187	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
196	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
197	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
200	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
201	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
202	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
203	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
204	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
205	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
206	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
207	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
208	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
209	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
210	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
211	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
212	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
213	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
214	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
215	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
216	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
217	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
218	C₄²×C₇	C₂⁴	1	16	yes	—
219	C₄²×C₇	C₂⁴	1	16	yes	—
220	C₄²×C₇	C₂⁴	1	16	yes	—
221	C₄²×C₇	C₂⁴	1	32	yes	—
222	C₂²×#41	C₂²×C₇	1	2	yes	—
223	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
224	#556	C₂²×C₇	1	64	yes	complemented
225	#555	C₂²×C₇	1	64	yes	complemented
226	#553	C₂²×C₇	1	64	yes	complemented
227	#552	C₂²×C₇	1	64	yes	complemented
228	#544	C₂²×C₇	1	16	yes	complemented
229	#538	C₂²×C₇	1	64	yes	complemented
230	#537	C₂²×C₇	1	16	yes	complemented
231	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	complemented
232	#529	C₂²×C₇	1	64	yes	complemented
233	C₂×#126	C₂²×C₇	1	8	yes	—
234	C₂×#126	C₂²×C₇	1	8	yes	complemented
235	C₂×#125	C₂²×C₇	1	4	yes	complemented
236	C₂×#125	C₂²×C₇	1	4	yes	complemented
237	C₂×#124	C₂²×C₇	1	8	yes	—
238	C₂×#124	C₂²×C₇	1	4	yes	complemented
239	#525	C₂²×C₇	1	32	yes	complemented
240	C₂×#123	C₂²×C₇	1	4	yes	—
241	C₂×#123	C₂²×C₇	1	8	yes	—
242	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
243	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
244	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
245	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
246	C₂×#121	C₂²×C₇	1	2	yes	—
247	C₂×#121	C₂²×C₇	1	2	yes	—
248	C₂×#121	C₂²×C₇	1	4	yes	—
249	C₂×#121	C₂²×C₇	1	8	yes	—
250	C₂×#121	C₂²×C₇	1	4	yes	complemented
251	C₂×#120	C₂²×C₇	1	4	yes	—
252	#520	C₂²×C₇	1	32	yes	complemented
253	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
254	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
255	C₂×C₄×D₄	C₂²×C₇	1	8	yes	—
256	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
257	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
258	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
259	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
260	C₂×#117	C₂²×C₇	1	4	yes	—
261	C₂×#117	C₂²×C₇	1	4	yes	—
262	C₂×#117	C₂²×C₇	1	2	yes	—
263	C₂×#117	C₂²×C₇	1	16	yes	complemented
264	C₂×#117	C₂²×C₇	1	4	yes	complemented
265	C₂×#117	C₂²×C₇	1	8	yes	complemented
266	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	complemented
269	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
270	C₂²×C₄²	C₂²×C₇	1	2	yes	—
271	C₂³×C₇	—	2	2	no	—
272	C₂³×C₇	—	2	2	no	—
273	C₂³×C₇	—	2	8	no	—
274	C₂³×C₇	—	2	4	no	—
275	C₂³×C₇	—	2	8	no	—
276	C₂³×C₇	—	2	8	no	—
277	C₂³×C₇	—	2	8	no	—
278	C₂³×C₇	—	2	4	no	—
279	C₂³×C₇	—	2	4	no	—
280	C₂³×C₇	—	4	4	no	—
281	C₂³×C₇	—	4	4	no	—
282	C₂³×C₇	—	4	16	no	—
283	C₂³×C₇	C₂×#41	1	4	yes	—
284	C₂³×C₇	C₂⁵	1	4	yes	—
285	C₂³×C₇	C₂⁵	1	8	yes	—
286	C₂³×C₇	C₂⁵	1	2	yes	—
287	C₂³×C₇	C₂⁵	1	1	yes	characteristic
288	C₇×Q₈	—	2	16	no	—
289	C₇×Q₈	—	4	16	no	—
290	C₇×D₄	—	2	32	no	—
291	C₇×D₄	—	2	16	no	—
292	C₇×D₄	—	4	16	no	—
293	C₇×D₄	—	4	16	no	—
294	C₇×D₄	—	4	16	no	—
295	C₂×C₄×C₇	—	2	8	no	—
296	C₂×C₄×C₇	—	2	2	no	—
297	C₂×C₄×C₇	—	2	2	no	—
298	C₂×C₄×C₇	—	2	8	no	—
299	C₂×C₄×C₇	—	2	8	no	—
300	C₂×C₄×C₇	—	2	8	no	—
301	C₂×C₄×C₇	—	2	8	no	—
302	C₂×C₄×C₇	—	2	8	no	—
303	C₂×C₄×C₇	—	2	16	no	—
304	C₂×C₄×C₇	—	2	16	no	—
305	C₂×C₄×C₇	—	2	32	no	—
306	C₂×C₄×C₇	—	4	8	no	—
307	C₂×C₄×C₇	—	4	32	no	—
308	C₂×C₄×C₇	—	4	8	no	—
309	C₂×C₄×C₇	C₂×#41	1	8	yes	—
310	C₂×C₄×C₇	C₂×#41	1	16	yes	—
311	C₂×C₄×C₇	C₂⁵	1	2	yes	—
312	C₂×C₄×C₇	C₂⁵	1	2	yes	—
313	C₂×C₄×C₇	C₂⁵	1	8	yes	—
314	C₂×C₄×C₇	C₂⁵	1	8	yes	—
315	C₂×C₄×C₇	C₂⁵	1	8	yes	—
316	C₂×C₄×C₇	C₂⁵	1	8	yes	—
317	C₂×C₄×C₇	C₂⁵	1	8	yes	—
318	C₂×C₄×C₇	C₂⁵	1	4	yes	—
319	C₂⁵	C₂³×C₇	1	1	yes	characteristic
320	C₂×#41	—	2	16	no	—
321	C₂×#41	C₂³×C₇	1	16	yes	—
322	C₂²×Q₈	C₂³×C₇	1	2	yes	—
323	C₂²×Q₈	C₂³×C₇	1	4	yes	—
324	C₂²×D₄	C₂³×C₇	1	4	yes	—
325	C₂²×D₄	C₂³×C₇	1	2	yes	—
326	C₂²×D₄	C₂³×C₇	1	4	yes	—
327	C₂²×D₄	C₂³×C₇	1	4	yes	—
328	C₂²×D₄	C₂³×C₇	1	4	yes	—
329	C₂³×C₄	—	2	8	no	—
330	C₂³×C₄	C₂³×C₇	1	4	yes	—
331	C₂³×C₄	C₂³×C₇	1	2	yes	—
332	C₂³×C₄	C₂³×C₇	1	2	yes	—
333	C₂³×C₄	C₂³×C₇	1	8	yes	—
334	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₇	1	2	yes	—
336	C₂³×C₄	C₂³×C₇	1	2	yes	—
337	C₂³×C₄	C₂³×C₇	1	8	yes	—
338	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
339	C₄⋊Q₈	C₂³×C₇	1	32	yes	complemented
340	#126	C₂³×C₇	1	64	yes	—
341	#126	C₂³×C₇	1	64	yes	complemented
342	#125	C₂³×C₇	1	32	yes	complemented
343	#125	C₂³×C₇	1	32	yes	complemented
344	#124	C₂³×C₇	1	64	yes	—
345	#124	C₂³×C₇	1	32	yes	complemented
346	#123	C₂³×C₇	1	32	yes	—
347	#123	C₂³×C₇	1	64	yes	—
348	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
349	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
350	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
351	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
352	#121	C₂³×C₇	1	16	yes	—
353	#121	C₂³×C₇	1	16	yes	—
354	#121	C₂³×C₇	1	32	yes	—
355	#121	C₂³×C₇	1	64	yes	—
356	#121	C₂³×C₇	1	32	yes	complemented
357	#120	C₂³×C₇	1	32	yes	—
358	C₄×Q₈	C₂³×C₇	1	32	yes	complemented
359	C₄×Q₈	C₂³×C₇	1	32	yes	complemented
360	C₄×D₄	C₂³×C₇	1	64	yes	—
361	C₄×D₄	C₂³×C₇	1	32	yes	—
362	C₄×D₄	C₂³×C₇	1	32	yes	—
363	C₄×D₄	C₂³×C₇	1	32	yes	complemented
364	C₄×D₄	C₂³×C₇	1	32	yes	complemented
365	#117	C₂³×C₇	1	32	yes	—
366	#117	C₂³×C₇	1	32	yes	—
367	#117	C₂³×C₇	1	16	yes	—
368	#117	C₂³×C₇	1	32	yes	complemented
369	#117	C₂³×C₇	1	64	yes	complemented
370	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
373	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
374	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
376	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
379	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	complemented
383	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
392	C₂×C₄²	C₂³×C₇	1	4	yes	—
393	C₂×C₄²	C₂³×C₇	1	4	yes	—
394	C₂×C₄²	C₂³×C₇	1	4	yes	—
395	C₂×C₄²	C₂³×C₇	1	8	yes	—
396	C₂×C₄²	C₂³×C₇	1	16	yes	—
397	C₂²×C₇	—	2	2	no	—
398	C₂²×C₇	—	2	2	no	—
399	C₂²×C₇	—	2	8	no	—
400	C₂²×C₇	—	2	4	no	—
401	C₂²×C₇	—	2	8	no	—
402	C₂²×C₇	—	2	8	no	—
403	C₂²×C₇	—	2	8	no	—
404	C₂²×C₇	—	2	4	no	—
405	C₂²×C₇	—	2	4	no	—
406	C₂²×C₇	—	4	16	no	—
407	C₂²×C₇	—	4	16	no	—
408	C₂²×C₇	—	4	8	no	—
409	C₂²×C₇	C₂²×#41	1	4	yes	—
410	C₂²×C₇	C₂²×#41	1	2	yes	—
411	C₂²×C₇	#585	1	2	yes	—
412	C₂²×C₇	#585	1	2	yes	—
413	C₂²×C₇	C₂⁶	1	1	yes	characteristic
414	C₄×C₇	—	2	2	no	—
415	C₄×C₇	—	2	2	no	—
416	C₄×C₇	—	2	8	no	—
417	C₄×C₇	—	2	8	no	—
418	C₄×C₇	—	2	8	no	—
419	C₄×C₇	—	2	8	no	—
420	C₄×C₇	—	2	8	no	—
421	C₄×C₇	C₂²×#41	1	8	yes	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	4	2	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	C₂⁴×C₇	1	2	yes	—
426	C₂⁴	C₂⁴×C₇	1	4	yes	—
427	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
428	C₂⁴	C₂⁴×C₇	1	4	yes	—
429	#41	—	2	64	no	—
430	C₂×Q₈	—	2	8	no	—
431	C₂×Q₈	—	4	8	no	—
432	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
433	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
434	C₂×D₄	—	2	16	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	4	8	no	—
437	C₂×D₄	—	4	8	no	—
438	C₂×D₄	—	4	8	no	—
439	C₂×D₄	C₂⁴×C₇	1	16	yes	—
440	C₂×D₄	C₂⁴×C₇	1	8	yes	—
441	C₂×D₄	C₂⁴×C₇	1	16	yes	—
442	C₂×D₄	C₂⁴×C₇	1	16	yes	—
443	C₂×D₄	C₂⁴×C₇	1	16	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	—	2	32	no	—
448	C₂²×C₄	—	2	16	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	16	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	C₇×#41	1	8	yes	—
453	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
462	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
463	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
464	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
465	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
466	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
467	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
470	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
471	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
472	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
473	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
474	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
475	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
476	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
477	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
478	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
479	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
480	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
481	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
482	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
483	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
484	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
485	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
486	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
487	C₄²	C₂⁴×C₇	1	16	yes	—
488	C₄²	C₂⁴×C₇	1	16	yes	—
489	C₄²	C₂⁴×C₇	1	16	yes	—
490	C₄²	C₂⁴×C₇	1	32	yes	—
491	C₂×C₇	—	2	4	no	—
492	C₂×C₇	—	4	8	no	—
493	C₂×C₇	—	4	4	no	—
494	C₂×C₇	#3493	1	4	yes	direct product factor
495	C₂×C₇	C₂³×#41	1	1	yes	characteristic
496	C₂×C₇	C₂×#585	1	1	yes	characteristic
497	C₂×C₇	C₂×#585	1	1	yes	characteristic
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	8	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	2	8	no	—
504	C₂³	—	2	8	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	4	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	16	no	—
510	C₂³	C₂×C₇×#41	1	4	yes	—
511	C₂³	C₂⁵×C₇	1	4	yes	—
512	C₂³	C₂⁵×C₇	1	8	yes	—
513	C₂³	C₂⁵×C₇	1	2	yes	—
514	C₂³	C₂⁵×C₇	1	1	yes	characteristic
515	Q₈	—	2	16	no	—
516	Q₈	—	4	16	no	—
517	D₄	—	2	32	no	—
518	D₄	—	2	16	no	—
519	D₄	—	4	16	no	—
520	D₄	—	4	16	no	—
521	D₄	—	4	16	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	16	no	—
531	C₂×C₄	—	2	16	no	—
532	C₂×C₄	—	2	32	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	—	4	32	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	C₂×C₇×#41	1	8	yes	—
537	C₂×C₄	C₂×C₇×#41	1	16	yes	—
538	C₂×C₄	C₂⁵×C₇	1	2	yes	—
539	C₂×C₄	C₂⁵×C₇	1	2	yes	—
540	C₂×C₄	C₂⁵×C₇	1	8	yes	—
541	C₂×C₄	C₂⁵×C₇	1	8	yes	—
542	C₂×C₄	C₂⁵×C₇	1	8	yes	—
543	C₂×C₄	C₂⁵×C₇	1	8	yes	—
544	C₂×C₄	C₂⁵×C₇	1	8	yes	—
545	C₂×C₄	C₂⁵×C₇	1	4	yes	—
546	C₇	C₂×#3493	1	1	yes	characteristic, direct product factor, Sylow
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	8	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	8	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	4	16	no	—
557	C₂²	—	4	8	no	—
558	C₂²	—	4	16	no	—
559	C₂²	C₂²×C₇×#41	1	4	yes	—
560	C₂²	C₂²×C₇×#41	1	2	yes	—
561	C₂²	C₇×#585	1	2	yes	—
562	C₂²	C₇×#585	1	2	yes	—
563	C₂²	C₂⁶×C₇	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	8	no	—
567	C₄	—	2	8	no	—
568	C₄	—	2	8	no	—
569	C₄	—	2	8	no	—
570	C₄	—	2	8	no	—
571	C₄	C₂²×C₇×#41	1	8	yes	—
572	C₂	—	2	4	no	—
573	C₂	—	4	4	no	—
574	C₂	—	4	8	no	—
575	C₂	C₇×#3493	1	4	yes	direct product factor
576	C₂	C₂³×C₇×#41	1	1	yes	characteristic
577	C₂	C₂×C₇×#585	1	1	yes	characteristic
578	C₂	C₂×C₇×#585	1	1	yes	characteristic

	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. C₇×#3493	C₂	direct (N × H)
2. C₂×C₇×#556	C₂	semidirect
3. C₂×C₇×#555	C₂	semidirect
4. C₂×C₇×#553	C₂	semidirect
5. C₂×C₇×#552	C₂	semidirect
6. C₂×C₇×#544	C₂	semidirect
7. C₂×C₇×#538	C₂	semidirect
8. C₂×C₇×#537	C₂	semidirect
9. C₂×C₇×#529	C₂	semidirect
10. C₂×C₇×#525	C₂	semidirect
11. C₂×C₇×#520	C₂	semidirect
12. C₂²×C₇×#117	C₂	semidirect
15. C₇×#556	C₂²	semidirect
16. C₇×#555	C₂²	semidirect
17. C₇×#553	C₂²	semidirect
18. C₇×#552	C₂²	semidirect
19. C₇×#544	C₂²	semidirect
20. C₇×#538	C₂²	semidirect
21. C₇×#537	C₂²	semidirect
22. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
23. C₇×#529	C₂²	semidirect
25. C₂×C₇×#126	C₂²	semidirect
26. C₂×C₇×#125	C₂²	semidirect
27. C₂×C₇×#125	C₂²	semidirect
29. C₂×C₇×#124	C₂²	semidirect
30. C₇×#525	C₂²	semidirect
36. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₇×#121	C₂²	semidirect
43. C₇×#520	C₂²	semidirect
44. C₂×C₄×C₇×Q₈	C₂²	semidirect
45. C₂×C₄×C₇×Q₈	C₂²	semidirect
49. C₂×C₄×C₇×D₄	C₂²	semidirect
50. C₂×C₄×C₇×D₄	C₂²	semidirect
54. C₂×C₇×#117	C₂²	semidirect
55. C₂×C₇×#117	C₂²	semidirect
56. C₂×C₇×#117	C₂²	semidirect
59. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
62. C₂×#3493	C₇	direct (N × H)
83. C₇×C₄⋊Q₈	C₂³	semidirect
85. C₇×#126	C₂³	semidirect
86. C₇×#125	C₂³	semidirect
87. C₇×#125	C₂³	semidirect
89. C₇×#124	C₂³	semidirect
95. C₇×C₂²⋊Q₈	C₂³	semidirect
100. C₇×#121	C₂³	semidirect
102. C₄×C₇×Q₈	C₂³	semidirect
103. C₄×C₇×Q₈	C₂³	semidirect
107. C₄×C₇×D₄	C₂³	semidirect
108. C₄×C₇×D₄	C₂³	semidirect
112. C₇×#117	C₂³	semidirect
113. C₇×#117	C₂³	semidirect
126. C₂×C₇×C₄⋊C₄	C₂³	semidirect
141. #3493	C₂×C₇	direct (N × H)
142. C₂×#556	C₂×C₇	semidirect
143. C₂×#555	C₂×C₇	semidirect
144. C₂×#553	C₂×C₇	semidirect
145. C₂×#552	C₂×C₇	semidirect
146. C₂×#544	C₂×C₇	semidirect
147. C₂×#538	C₂×C₇	semidirect
148. C₂×#537	C₂×C₇	semidirect
149. C₂×#529	C₂×C₇	semidirect
150. C₂×#525	C₂×C₇	semidirect
151. C₂×#520	C₂×C₇	semidirect
152. C₂²×#117	C₂×C₇	semidirect
224. #556	C₂²×C₇	semidirect
225. #555	C₂²×C₇	semidirect
226. #553	C₂²×C₇	semidirect
227. #552	C₂²×C₇	semidirect
228. #544	C₂²×C₇	semidirect
229. #538	C₂²×C₇	semidirect
230. #537	C₂²×C₇	semidirect
231. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
232. #529	C₂²×C₇	semidirect
234. C₂×#126	C₂²×C₇	semidirect
235. C₂×#125	C₂²×C₇	semidirect
236. C₂×#125	C₂²×C₇	semidirect
238. C₂×#124	C₂²×C₇	semidirect
239. #525	C₂²×C₇	semidirect
245. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
250. C₂×#121	C₂²×C₇	semidirect
252. #520	C₂²×C₇	semidirect
253. C₂×C₄×Q₈	C₂²×C₇	semidirect
254. C₂×C₄×Q₈	C₂²×C₇	semidirect
258. C₂×C₄×D₄	C₂²×C₇	semidirect
259. C₂×C₄×D₄	C₂²×C₇	semidirect
263. C₂×#117	C₂²×C₇	semidirect
264. C₂×#117	C₂²×C₇	semidirect
265. C₂×#117	C₂²×C₇	semidirect
268. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
339. C₄⋊Q₈	C₂³×C₇	semidirect
341. #126	C₂³×C₇	semidirect
342. #125	C₂³×C₇	semidirect
343. #125	C₂³×C₇	semidirect
345. #124	C₂³×C₇	semidirect
351. C₂²⋊Q₈	C₂³×C₇	semidirect
356. #121	C₂³×C₇	semidirect
358. C₄×Q₈	C₂³×C₇	semidirect
359. C₄×Q₈	C₂³×C₇	semidirect
363. C₄×D₄	C₂³×C₇	semidirect
364. C₄×D₄	C₂³×C₇	semidirect
368. #117	C₂³×C₇	semidirect
369. #117	C₂³×C₇	semidirect
382. C₂×C₄⋊C₄	C₂³×C₇	semidirect
494. C₂×C₇	#3493	direct (N × H)
546. C₇	C₂×#3493	direct (N × H)
575. C₂	C₇×#3493	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3493	2
C₂×C₇×#556	2
C₂×C₇×#555	2
C₂×C₇×#553	2
C₂×C₇×#552	2
C₂×C₇×#544	2
C₂×C₇×#538	2
C₂×C₇×#537	2
C₂×C₇×#529	2
C₂×C₇×#525	2
C₂×C₇×#520	2
C₂²×C₇×#117	2
C₂×#3493	7

Subgroups — C2×C7×#3493 #13239992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3493 #13239992