Subgroups — C₇×#60212 #13237428

Order 1792.

1874 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3455	C₂	1	1	yes	maximal, characteristic
2	C₇×#2969	C₂	1	4	yes	maximal, complemented
3	C₇×#2968	C₂	1	4	yes	maximal, complemented
4	C₇×#2967	C₂	1	4	yes	maximal, complemented
5	C₇×#2966	C₂	1	4	yes	maximal, complemented
6	C₇×#2962	C₂	1	2	yes	maximal, complemented
7	C₇×#2935	C₂	1	2	yes	maximal, complemented
8	C₇×#2933	C₂	1	2	yes	maximal, complemented
9	C₇×#2933	C₂	1	2	yes	maximal, complemented
10	C₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#131	C₂²	1	2	yes	—
17	C₂×C₇×#131	C₂²	1	2	yes	—
18	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
19	C₇×#542	C₄	1	2	yes	—
20	C₇×#542	C₄	1	2	yes	—
21	C₇×#541	C₄	1	2	yes	—
22	C₇×#540	C₄	1	2	yes	—
23	C₇×#539	C₄	1	4	yes	—
24	C₇×#538	C₄	1	4	yes	—
25	C₇×#533	C₂²	1	1	yes	characteristic
26	C₇×#532	C₂²	1	1	yes	characteristic
27	C₇×#529	C₂²	1	4	yes	—
28	C₇×#529	C₂²	1	4	yes	—
29	C₇×#525	C₂²	1	1	yes	characteristic
30	C₇×#525	C₂²	1	1	yes	characteristic
31	C₄×C₇×#41	C₂²	1	1	yes	characteristic
32	C₄×C₇×#41	C₂²	1	1	yes	characteristic
33	C₂×C₇×#117	C₂²	1	1	yes	characteristic
34	C₇×#446	C₂²	1	4	yes	complemented
35	C₇×#446	C₂²	1	4	yes	complemented
36	C₇×#446	C₂²	1	4	yes	complemented
37	C₇×C₈×Q₈	C₂²	1	4	yes	complemented
38	C₇×#436	C₂²	1	4	yes	—
39	C₇×#436	C₂²	1	4	yes	—
40	C₇×#436	C₂²	1	4	yes	complemented
41	C₇×#435	C₂²	1	4	yes	—
42	C₇×#435	C₂²	1	4	yes	—
43	C₇×#435	C₂²	1	4	yes	—
44	C₇×#435	C₂²	1	4	yes	—
45	C₇×#435	C₂²	1	4	yes	complemented
46	C₇×#435	C₂²	1	4	yes	complemented
47	C₇×C₈×D₄	C₂²	1	4	yes	—
48	C₇×C₈×D₄	C₂²	1	4	yes	—
49	C₇×C₈×D₄	C₂²	1	4	yes	complemented
50	C₇×#433	C₂²	1	2	yes	—
51	C₇×#433	C₂²	1	2	yes	—
52	C₇×#433	C₂²	1	2	yes	—
53	C₇×#433	C₂²	1	2	yes	—
54	C₇×#433	C₂²	1	2	yes	complemented
55	C₇×#433	C₂²	1	2	yes	complemented
56	C₇×#433	C₂²	1	2	yes	complemented
57	C₇×#433	C₂²	1	2	yes	complemented
58	C₇×#432	C₂²	1	4	yes	complemented
59	C₇×#431	C₂²	1	4	yes	complemented
60	C₇×#424	C₂²	1	2	yes	—
61	C₇×#424	C₂²	1	2	yes	—
62	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
63	C₇×#408	C₂²	1	2	yes	—
64	C₇×#408	C₂²	1	2	yes	—
65	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
66	C₇×#405	C₂²	1	2	yes	—
67	C₇×#405	C₂²	1	2	yes	—
68	C₇×#405	C₂²	1	4	yes	—
69	C₇×#405	C₂²	1	4	yes	—
70	C₇×#405	C₂²	1	4	yes	complemented
71	C₇×#405	C₂²	1	4	yes	complemented
72	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
73	C₄×C₇×M₁₆	C₂²	1	2	yes	—
74	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
75	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
76	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
77	C₂×C₇×#97	C₂²	1	1	yes	characteristic
78	C₂×C₇×#97	C₂²	1	2	yes	complemented
79	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
81	#60212	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂×C₇×#41	C₂³	1	1	yes	characteristic
83	C₂×C₇×#41	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
85	C₇×#131	—	2	8	no	—
86	C₇×#131	—	2	8	no	—
87	C₂×C₇×M₁₆	—	2	8	no	—
88	C₂×C₇×M₁₆	C₂³	1	2	yes	—
89	C₂×C₇×M₁₆	C₂³	1	4	yes	—
90	C₂×C₇×M₁₆	C₂³	1	4	yes	—
91	C₂×C₇×M₁₆	C₂³	1	4	yes	—
92	C₂×C₇×M₁₆	C₂³	1	2	yes	—
93	C₂²×C₇×C₈	C₂³	1	2	yes	—
94	C₂²×C₇×C₈	C₂³	1	4	yes	—
95	C₂²×C₇×C₈	C₂³	1	2	yes	—
96	C₂²×C₇×C₈	C₂³	1	4	yes	—
97	C₂²×C₇×C₈	C₂³	1	4	yes	—
98	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
99	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
100	C₇×#127	C₂×C₄	1	1	yes	characteristic
101	C₇×#126	C₂×C₄	1	4	yes	—
102	C₇×#126	C₂×C₄	1	4	yes	—
103	C₇×#126	C₂×C₄	1	4	yes	—
104	C₇×#126	C₂×C₄	1	4	yes	—
105	C₇×#125	C₂×C₄	1	4	yes	—
106	C₇×#125	C₂×C₄	1	4	yes	—
107	C₇×#125	C₂×C₄	1	2	yes	—
108	C₇×#124	C₂×C₄	1	4	yes	—
109	C₇×#124	C₂×C₄	1	4	yes	—
110	C₇×#124	C₂×C₄	1	1	yes	characteristic
111	C₇×#124	C₂×C₄	1	1	yes	characteristic
112	C₇×#123	C₂×C₄	1	2	yes	—
113	C₇×#123	C₂×C₄	1	2	yes	—
114	C₇×#123	C₂×C₄	1	4	yes	—
115	C₇×#123	C₂×C₄	1	4	yes	—
116	C₇×#123	C₂×C₄	1	4	yes	—
117	C₇×#123	C₂×C₄	1	4	yes	—
118	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
119	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
120	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
121	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
122	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
123	C₇×#121	C₂×C₄	1	2	yes	—
124	C₇×#121	C₂×C₄	1	2	yes	—
125	C₇×#121	C₂×C₄	1	4	yes	—
126	C₇×#121	C₂×C₄	1	4	yes	—
127	C₇×#121	C₂×C₄	1	4	yes	—
128	C₇×#120	C₂×C₄	1	2	yes	—
129	C₇×#120	C₂×C₄	1	2	yes	—
130	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
131	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
132	C₄×C₇×Q₈	C₂³	1	4	yes	—
133	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
134	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
135	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
136	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
137	C₄×C₇×D₄	C₂³	1	4	yes	—
138	C₄×C₇×D₄	C₂³	1	4	yes	—
139	C₄×C₇×D₄	C₂³	1	4	yes	—
140	C₇×#117	C₂×C₄	1	2	yes	—
141	C₇×#117	C₂×C₄	1	2	yes	—
142	C₇×#117	C₂³	1	2	yes	—
143	C₇×#117	C₂³	1	2	yes	—
144	C₇×#117	C₂³	1	1	yes	characteristic
145	C₇×#117	C₂³	1	1	yes	characteristic
146	C₇×#117	C₂³	1	2	yes	—
147	C₇×#117	C₂³	1	2	yes	—
148	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
149	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
150	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₇	C₂³	1	2	yes	—
153	C₂×C₄²×C₇	C₂³	1	2	yes	—
154	C₇×C₄⋊C₈	C₂³	1	2	yes	—
155	C₇×C₄⋊C₈	C₂³	1	2	yes	—
156	C₇×C₄⋊C₈	C₂³	1	2	yes	—
157	C₇×C₄⋊C₈	C₂³	1	2	yes	—
158	C₇×C₄⋊C₈	C₂³	1	4	yes	—
159	C₇×C₄⋊C₈	C₂³	1	4	yes	—
160	C₇×C₄⋊C₈	C₂³	1	4	yes	—
161	C₇×C₄⋊C₈	C₂³	1	4	yes	—
162	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
163	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
164	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
165	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
166	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
167	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
168	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
169	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
170	C₇×#97	C₂³	1	1	yes	characteristic
171	C₇×#97	C₂³	1	1	yes	characteristic
172	C₇×#97	C₂³	1	2	yes	—
173	C₇×#97	C₂³	1	2	yes	—
174	C₇×#97	C₂³	1	4	yes	—
175	C₇×#97	C₂³	1	2	yes	—
176	C₇×#97	C₂³	1	4	yes	—
177	C₇×#97	C₂³	1	4	yes	—
178	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
179	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
180	C₄×C₇×C₈	C₂³	1	2	yes	—
181	C₄×C₇×C₈	C₂³	1	2	yes	—
182	C₄×C₇×C₈	C₂³	1	4	yes	—
183	C₄×C₇×C₈	C₂³	1	2	yes	—
184	C₄×C₇×C₈	C₂³	1	4	yes	—
185	C₄×C₇×C₈	C₂³	1	4	yes	—
186	#3455	C₂×C₇	1	1	yes	characteristic
187	#2969	C₂×C₇	1	4	yes	complemented
188	#2968	C₂×C₇	1	4	yes	complemented
189	#2967	C₂×C₇	1	4	yes	complemented
190	#2966	C₂×C₇	1	4	yes	complemented
191	#2962	C₂×C₇	1	2	yes	complemented
192	#2935	C₂×C₇	1	2	yes	complemented
193	#2933	C₂×C₇	1	2	yes	complemented
194	#2933	C₂×C₇	1	2	yes	complemented
195	#2923	C₂×C₇	1	1	yes	characteristic, complemented
196	#2922	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
198	#2875	C₂×C₇	1	1	yes	characteristic, complemented
199	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
200	#2873	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
202	C₇×#41	—	2	4	no	—
203	C₇×#41	—	2	4	no	—
204	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
207	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
208	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
209	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
212	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
213	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
214	C₂²×C₄×C₇	—	2	4	no	—
215	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
217	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
218	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
219	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
220	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
221	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
225	C₇×M₁₆	—	2	4	no	—
226	C₇×M₁₆	—	2	8	no	—
227	C₇×M₁₆	—	2	8	no	—
228	C₇×M₁₆	—	2	8	no	—
229	C₇×M₁₆	#41	1	8	yes	—
230	C₂×C₇×C₈	—	2	4	no	—
231	C₂×C₇×C₈	—	2	4	no	—
232	C₂×C₇×C₈	—	2	8	no	—
233	C₂×C₇×C₈	—	2	8	no	—
234	C₂×C₇×C₈	—	2	8	no	—
235	C₂×C₇×C₈	C₂⁴	1	2	yes	—
236	C₂×C₇×C₈	C₂⁴	1	2	yes	—
237	C₂×C₇×C₈	C₂⁴	1	4	yes	—
238	C₂×C₇×C₈	C₂⁴	1	2	yes	—
239	C₂×C₇×C₈	C₂⁴	1	2	yes	—
240	C₂×C₇×C₈	C₂⁴	1	4	yes	—
241	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
242	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
243	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
244	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
245	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
246	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
247	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
248	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
249	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
250	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
251	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
252	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
253	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
254	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
255	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
256	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
257	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
258	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
259	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
260	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
261	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
262	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
263	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
264	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
265	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
266	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
267	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
268	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
269	C₄²×C₇	C₂²×C₄	1	2	yes	—
270	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
271	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
272	C₄²×C₇	C₂²×C₄	1	4	yes	—
273	C₄²×C₇	C₂²×C₄	1	4	yes	—
274	C₄²×C₇	C₂⁴	1	1	yes	characteristic
275	C₄²×C₇	C₂⁴	1	1	yes	characteristic
276	C₄²×C₇	C₂⁴	1	2	yes	—
277	C₄²×C₇	C₂⁴	1	2	yes	—
278	C₄²×C₇	C₂⁴	1	2	yes	—
279	C₂×#131	C₂²×C₇	1	2	yes	—
280	C₂×#131	C₂²×C₇	1	2	yes	—
281	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
282	#542	C₄×C₇	1	2	yes	—
283	#542	C₄×C₇	1	2	yes	—
284	#541	C₄×C₇	1	2	yes	—
285	#540	C₄×C₇	1	2	yes	—
286	#539	C₄×C₇	1	4	yes	—
287	#538	C₄×C₇	1	4	yes	—
288	#533	C₂²×C₇	1	1	yes	characteristic
289	#532	C₂²×C₇	1	1	yes	characteristic
290	#529	C₂²×C₇	1	4	yes	—
291	#529	C₂²×C₇	1	4	yes	—
292	#525	C₂²×C₇	1	1	yes	characteristic
293	#525	C₂²×C₇	1	1	yes	characteristic
294	C₄×#41	C₂²×C₇	1	1	yes	characteristic
295	C₄×#41	C₂²×C₇	1	1	yes	characteristic
296	C₂×#117	C₂²×C₇	1	1	yes	characteristic
297	#446	C₂²×C₇	1	4	yes	complemented
298	#446	C₂²×C₇	1	4	yes	complemented
299	#446	C₂²×C₇	1	4	yes	complemented
300	C₈×Q₈	C₂²×C₇	1	4	yes	complemented
301	#436	C₂²×C₇	1	4	yes	—
302	#436	C₂²×C₇	1	4	yes	—
303	#436	C₂²×C₇	1	4	yes	complemented
304	#435	C₂²×C₇	1	4	yes	—
305	#435	C₂²×C₇	1	4	yes	—
306	#435	C₂²×C₇	1	4	yes	—
307	#435	C₂²×C₇	1	4	yes	—
308	#435	C₂²×C₇	1	4	yes	complemented
309	#435	C₂²×C₇	1	4	yes	complemented
310	C₈×D₄	C₂²×C₇	1	4	yes	—
311	C₈×D₄	C₂²×C₇	1	4	yes	—
312	C₈×D₄	C₂²×C₇	1	4	yes	complemented
313	#433	C₂²×C₇	1	2	yes	—
314	#433	C₂²×C₇	1	2	yes	—
315	#433	C₂²×C₇	1	2	yes	—
316	#433	C₂²×C₇	1	2	yes	—
317	#433	C₂²×C₇	1	2	yes	complemented
318	#433	C₂²×C₇	1	2	yes	complemented
319	#433	C₂²×C₇	1	2	yes	complemented
320	#433	C₂²×C₇	1	2	yes	complemented
321	#432	C₂²×C₇	1	4	yes	complemented
322	#431	C₂²×C₇	1	4	yes	complemented
323	#424	C₂²×C₇	1	2	yes	—
324	#424	C₂²×C₇	1	2	yes	—
325	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
326	#408	C₂²×C₇	1	2	yes	—
327	#408	C₂²×C₇	1	2	yes	—
328	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
329	#405	C₂²×C₇	1	4	yes	—
330	#405	C₂²×C₇	1	4	yes	—
331	#405	C₂²×C₇	1	2	yes	—
332	#405	C₂²×C₇	1	2	yes	—
333	#405	C₂²×C₇	1	4	yes	complemented
334	#405	C₂²×C₇	1	4	yes	complemented
335	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
336	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
337	C₄×M₁₆	C₂²×C₇	1	2	yes	—
338	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
339	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
340	C₂×#97	C₂²×C₇	1	1	yes	characteristic
341	C₂×#97	C₂²×C₇	1	2	yes	complemented
342	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
343	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
344	C₂³×C₇	—	2	2	no	—
345	C₂³×C₇	—	4	2	no	—
346	C₂³×C₇	C₂³×C₄	1	2	yes	—
347	C₂³×C₇	C₂³×C₄	1	2	yes	—
348	C₂³×C₇	C₂³×C₄	1	2	yes	—
349	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
350	C₇×Q₈	—	2	2	no	—
351	C₇×Q₈	—	2	2	no	—
352	C₇×Q₈	—	4	4	no	—
353	C₇×D₄	—	2	4	no	—
354	C₇×D₄	—	2	4	no	—
355	C₇×D₄	—	2	2	no	—
356	C₇×D₄	—	2	2	no	—
357	C₇×D₄	—	4	4	no	—
358	C₇×D₄	—	4	4	no	—
359	C₇×D₄	—	4	4	no	—
360	C₂×C₄×C₇	—	2	2	no	—
361	C₂×C₄×C₇	—	2	4	no	—
362	C₂×C₄×C₇	—	2	2	no	—
363	C₂×C₄×C₇	—	2	4	no	—
364	C₂×C₄×C₇	—	2	4	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	4	2	no	—
367	C₂×C₄×C₇	—	4	4	no	—
368	C₂×C₄×C₇	—	4	4	no	—
369	C₂×C₄×C₇	—	4	2	no	—
370	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
371	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
372	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
373	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
374	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
375	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
376	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
377	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
378	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
379	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
380	C₂×C₄×C₇	C₂×#41	1	4	yes	—
381	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
382	C₇×C₈	—	2	2	no	—
383	C₇×C₈	—	2	2	no	—
384	C₇×C₈	—	2	2	no	—
385	C₇×C₈	—	2	2	no	—
386	C₇×C₈	—	2	4	no	—
387	C₇×C₈	C₂×#41	1	8	yes	—
388	C₂×#41	C₂³×C₇	1	1	yes	characteristic
389	C₂×#41	C₂³×C₇	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
391	#131	—	2	8	no	—
392	#131	—	2	8	no	—
393	C₂×M₁₆	—	2	8	no	—
394	C₂×M₁₆	C₂³×C₇	1	2	yes	—
395	C₂×M₁₆	C₂³×C₇	1	4	yes	—
396	C₂×M₁₆	C₂³×C₇	1	4	yes	—
397	C₂×M₁₆	C₂³×C₇	1	4	yes	—
398	C₂×M₁₆	C₂³×C₇	1	2	yes	—
399	C₂²×C₈	C₂³×C₇	1	4	yes	—
400	C₂²×C₈	C₂³×C₇	1	2	yes	—
401	C₂²×C₈	C₂³×C₇	1	4	yes	—
402	C₂²×C₈	C₂³×C₇	1	2	yes	—
403	C₂²×C₈	C₂³×C₇	1	4	yes	—
404	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
405	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
406	#127	C₂×C₄×C₇	1	1	yes	characteristic
407	#126	C₂×C₄×C₇	1	4	yes	—
408	#126	C₂×C₄×C₇	1	4	yes	—
409	#126	C₂×C₄×C₇	1	4	yes	—
410	#126	C₂×C₄×C₇	1	4	yes	—
411	#125	C₂×C₄×C₇	1	4	yes	—
412	#125	C₂×C₄×C₇	1	4	yes	—
413	#125	C₂×C₄×C₇	1	2	yes	—
414	#124	C₂×C₄×C₇	1	4	yes	—
415	#124	C₂×C₄×C₇	1	4	yes	—
416	#124	C₂×C₄×C₇	1	1	yes	characteristic
417	#124	C₂×C₄×C₇	1	1	yes	characteristic
418	#123	C₂×C₄×C₇	1	2	yes	—
419	#123	C₂×C₄×C₇	1	2	yes	—
420	#123	C₂×C₄×C₇	1	4	yes	—
421	#123	C₂×C₄×C₇	1	4	yes	—
422	#123	C₂×C₄×C₇	1	4	yes	—
423	#123	C₂×C₄×C₇	1	4	yes	—
424	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
425	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
426	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
427	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
428	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
429	#121	C₂×C₄×C₇	1	2	yes	—
430	#121	C₂×C₄×C₇	1	2	yes	—
431	#121	C₂×C₄×C₇	1	4	yes	—
432	#121	C₂×C₄×C₇	1	4	yes	—
433	#121	C₂×C₄×C₇	1	4	yes	—
434	#120	C₂×C₄×C₇	1	2	yes	—
435	#120	C₂×C₄×C₇	1	2	yes	—
436	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
437	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
438	C₄×Q₈	C₂³×C₇	1	4	yes	—
439	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
440	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
441	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
442	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
443	C₄×D₄	C₂³×C₇	1	4	yes	—
444	C₄×D₄	C₂³×C₇	1	4	yes	—
445	C₄×D₄	C₂³×C₇	1	4	yes	—
446	#117	C₂×C₄×C₇	1	2	yes	—
447	#117	C₂×C₄×C₇	1	2	yes	—
448	#117	C₂³×C₇	1	2	yes	—
449	#117	C₂³×C₇	1	2	yes	—
450	#117	C₂³×C₇	1	1	yes	characteristic
451	#117	C₂³×C₇	1	1	yes	characteristic
452	#117	C₂³×C₇	1	2	yes	—
453	#117	C₂³×C₇	1	2	yes	—
454	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
456	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
457	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₇	1	2	yes	—
459	C₂×C₄²	C₂³×C₇	1	2	yes	—
460	C₄⋊C₈	C₂³×C₇	1	2	yes	—
461	C₄⋊C₈	C₂³×C₇	1	2	yes	—
462	C₄⋊C₈	C₂³×C₇	1	2	yes	—
463	C₄⋊C₈	C₂³×C₇	1	2	yes	—
464	C₄⋊C₈	C₂³×C₇	1	4	yes	—
465	C₄⋊C₈	C₂³×C₇	1	4	yes	—
466	C₄⋊C₈	C₂³×C₇	1	4	yes	—
467	C₄⋊C₈	C₂³×C₇	1	4	yes	—
468	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
469	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
470	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
471	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
472	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
473	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
474	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
475	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
476	#97	C₂³×C₇	1	1	yes	characteristic
477	#97	C₂³×C₇	1	1	yes	characteristic
478	#97	C₂³×C₇	1	2	yes	—
479	#97	C₂³×C₇	1	2	yes	—
480	#97	C₂³×C₇	1	4	yes	—
481	#97	C₂³×C₇	1	2	yes	—
482	#97	C₂³×C₇	1	4	yes	—
483	#97	C₂³×C₇	1	4	yes	—
484	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
485	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
486	C₄×C₈	C₂³×C₇	1	2	yes	—
487	C₄×C₈	C₂³×C₇	1	2	yes	—
488	C₄×C₈	C₂³×C₇	1	4	yes	—
489	C₄×C₈	C₂³×C₇	1	2	yes	—
490	C₄×C₈	C₂³×C₇	1	4	yes	—
491	C₄×C₈	C₂³×C₇	1	4	yes	—
492	C₂²×C₇	—	2	2	no	—
493	C₂²×C₇	—	2	2	no	—
494	C₂²×C₇	—	2	2	no	—
495	C₂²×C₇	—	2	2	no	—
496	C₂²×C₇	—	2	4	no	—
497	C₂²×C₇	—	2	4	no	—
498	C₂²×C₇	—	2	2	no	—
499	C₂²×C₇	—	2	2	no	—
500	C₂²×C₇	—	8	2	no	—
501	C₂²×C₇	C₄×#41	1	2	yes	—
502	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
503	C₄×C₇	—	2	2	no	—
504	C₄×C₇	—	2	2	no	—
505	C₄×C₇	—	2	2	no	—
506	C₄×C₇	—	2	2	no	—
507	C₄×C₇	—	2	2	no	—
508	C₄×C₇	—	2	2	no	—
509	C₄×C₇	—	2	4	no	—
510	C₄×C₇	—	2	4	no	—
511	C₄×C₇	—	2	2	no	—
512	C₄×C₇	C₄×#41	1	2	yes	—
513	C₄×C₇	C₂²×#41	1	2	yes	—
514	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
515	#41	—	2	4	no	—
516	#41	—	2	4	no	—
517	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
518	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
519	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
520	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
521	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
522	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
523	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
524	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
525	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
526	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
530	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
531	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
532	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
533	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
534	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
538	M₁₆	—	2	4	no	—
539	M₁₆	—	2	8	no	—
540	M₁₆	—	2	8	no	—
541	M₁₆	—	2	8	no	—
542	M₁₆	C₇×#41	1	8	yes	—
543	C₂×C₈	—	2	4	no	—
544	C₂×C₈	—	2	4	no	—
545	C₂×C₈	—	2	8	no	—
546	C₂×C₈	—	2	8	no	—
547	C₂×C₈	—	2	8	no	—
548	C₂×C₈	C₂⁴×C₇	1	2	yes	—
549	C₂×C₈	C₂⁴×C₇	1	2	yes	—
550	C₂×C₈	C₂⁴×C₇	1	4	yes	—
551	C₂×C₈	C₂⁴×C₇	1	2	yes	—
552	C₂×C₈	C₂⁴×C₇	1	2	yes	—
553	C₂×C₈	C₂⁴×C₇	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
555	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
556	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
557	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
558	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
559	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
560	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
562	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
563	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
564	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
565	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
566	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
567	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
570	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
572	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
582	C₄²	C₂²×C₄×C₇	1	2	yes	—
583	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
584	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
585	C₄²	C₂²×C₄×C₇	1	4	yes	—
586	C₄²	C₂²×C₄×C₇	1	4	yes	—
587	C₄²	C₂⁴×C₇	1	1	yes	characteristic
588	C₄²	C₂⁴×C₇	1	1	yes	characteristic
589	C₄²	C₂⁴×C₇	1	2	yes	—
590	C₄²	C₂⁴×C₇	1	2	yes	—
591	C₄²	C₂⁴×C₇	1	2	yes	—
592	C₂×C₇	—	2	2	no	—
593	C₂×C₇	—	4	2	no	—
594	C₂×C₇	—	4	2	no	—
595	C₂×C₇	—	4	2	no	—
596	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
597	C₂×C₇	#3573	1	2	yes	—
598	C₂³	—	2	2	no	—
599	C₂³	—	4	2	no	—
600	C₂³	C₂³×C₄×C₇	1	2	yes	—
601	C₂³	C₂³×C₄×C₇	1	2	yes	—
602	C₂³	C₂³×C₄×C₇	1	2	yes	—
603	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
604	Q₈	—	2	2	no	—
605	Q₈	—	2	2	no	—
606	Q₈	—	4	4	no	—
607	D₄	—	2	4	no	—
608	D₄	—	2	4	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	4	4	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	4	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
627	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
628	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
629	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
630	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
632	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
634	C₂×C₄	C₂×C₇×#41	1	4	yes	—
635	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
636	C₈	—	2	2	no	—
637	C₈	—	2	2	no	—
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	2	4	no	—
641	C₈	C₂×C₇×#41	1	8	yes	—
642	C₇	#60212	1	1	yes	characteristic, direct product factor, Sylow
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	8	2	no	—
652	C₂²	C₄×C₇×#41	1	2	yes	—
653	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	C₄×C₇×#41	1	2	yes	—
664	C₄	C₂²×C₇×#41	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	4	2	no	—
669	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
670	C₂	C₇×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂⁴×C₄
prime radical	C₇×#3455	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2969	C₂	semidirect
3. C₇×#2968	C₂	semidirect
4. C₇×#2967	C₂	semidirect
5. C₇×#2966	C₂	semidirect
6. C₇×#2962	C₂	semidirect
7. C₇×#2935	C₂	semidirect
8. C₇×#2933	C₂	semidirect
9. C₇×#2933	C₂	semidirect
10. C₇×#2923	C₂	semidirect
11. C₇×#2922	C₂	semidirect
12. C₂×C₇×#433	C₂	semidirect
13. C₇×#2875	C₂	semidirect
14. C₄×C₇×#131	C₂	semidirect
15. C₇×#2873	C₂	semidirect
34. C₇×#446	C₂²	semidirect
35. C₇×#446	C₂²	semidirect
36. C₇×#446	C₂²	semidirect
37. C₇×C₈×Q₈	C₂²	semidirect
40. C₇×#436	C₂²	semidirect
45. C₇×#435	C₂²	semidirect
46. C₇×#435	C₂²	semidirect
49. C₇×C₈×D₄	C₂²	semidirect
54. C₇×#433	C₂²	semidirect
55. C₇×#433	C₂²	semidirect
56. C₇×#433	C₂²	semidirect
57. C₇×#433	C₂²	semidirect
58. C₇×#432	C₂²	semidirect
59. C₇×#431	C₂²	semidirect
70. C₇×#405	C₂²	semidirect
71. C₇×#405	C₂²	semidirect
75. C₄×C₇×M₁₆	C₂²	semidirect
76. C₄×C₇×M₁₆	C₂²	semidirect
78. C₂×C₇×#97	C₂²	semidirect
80. C₂×C₄×C₇×C₈	C₂²	semidirect
81. #60212	C₇	direct (N × H)
187. #2969	C₂×C₇	semidirect
188. #2968	C₂×C₇	semidirect
189. #2967	C₂×C₇	semidirect
190. #2966	C₂×C₇	semidirect
191. #2962	C₂×C₇	semidirect
192. #2935	C₂×C₇	semidirect
193. #2933	C₂×C₇	semidirect
194. #2933	C₂×C₇	semidirect
195. #2923	C₂×C₇	semidirect
196. #2922	C₂×C₇	semidirect
197. C₂×#433	C₂×C₇	semidirect
198. #2875	C₂×C₇	semidirect
199. C₄×#131	C₂×C₇	semidirect
200. #2873	C₂×C₇	semidirect
297. #446	C₂²×C₇	semidirect
298. #446	C₂²×C₇	semidirect
299. #446	C₂²×C₇	semidirect
300. C₈×Q₈	C₂²×C₇	semidirect
303. #436	C₂²×C₇	semidirect
308. #435	C₂²×C₇	semidirect
309. #435	C₂²×C₇	semidirect
312. C₈×D₄	C₂²×C₇	semidirect
317. #433	C₂²×C₇	semidirect
318. #433	C₂²×C₇	semidirect
319. #433	C₂²×C₇	semidirect
320. #433	C₂²×C₇	semidirect
321. #432	C₂²×C₇	semidirect
322. #431	C₂²×C₇	semidirect
333. #405	C₂²×C₇	semidirect
334. #405	C₂²×C₇	semidirect
338. C₄×M₁₆	C₂²×C₇	semidirect
339. C₄×M₁₆	C₂²×C₇	semidirect
341. C₂×#97	C₂²×C₇	semidirect
343. C₂×C₄×C₈	C₂²×C₇	semidirect
642. C₇	#60212	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×#3455	2
C₇×#2969	2
C₇×#2968	2
C₇×#2967	2
C₇×#2966	2
C₇×#2962	2
C₇×#2935	2
C₇×#2933	2
C₇×#2923	2
C₇×#2922	2
C₂×C₇×#433	2
C₇×#2875	2
C₄×C₇×#131	2
C₇×#2873	2
#60212	7

Subgroups — C7×#60212 #13237428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60212 #13237428