Subgroups — C₇×#60622 #13237838

Order 1792.

2178 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3498	C₂	1	1	yes	maximal, characteristic
3	C₇×#3141	C₂	1	3	yes	maximal, complemented
4	C₇×#3138	C₂	1	3	yes	maximal, complemented
5	C₇×#3136	C₂	1	12	yes	maximal, complemented
6	C₇×#3131	C₂	1	3	yes	maximal, complemented
7	C₂×C₇×#486	C₂	1	3	yes	maximal, complemented
8	C₇×#2897	C₂	1	4	yes	maximal, complemented
9	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
11	C₂×C₇×#131	C₂²	1	2	yes	—
12	C₇×Q₈²	—	2	1	no	—
13	C₇×#557	—	2	1	no	—
14	C₇×#554	—	2	3	no	—
15	C₇×#550	—	2	1	no	—
16	C₇×#550	—	2	1	no	—
17	C₇×D₄×Q₈	—	2	3	no	—
18	C₇×D₄²	—	2	3	no	—
19	C₇×D₄²	—	2	3	no	—
20	C₇×#544	C₂²	1	6	yes	complemented
21	C₇×#535	C₂²	1	6	yes	—
22	C₇×#533	C₂²	1	3	yes	complemented
23	C₇×#532	C₂²	1	3	yes	—
24	C₂×C₇×C₄⋊Q₈	C₂²	1	3	yes	complemented
25	C₂×C₇×#127	C₂²	1	3	yes	—
26	C₇×#520	C₂²	1	2	yes	—
27	C₄×C₇×#41	C₂²	1	1	yes	characteristic
28	C₇×#490	C₂²	1	12	yes	complemented
29	C₇×#489	C₂²	1	12	yes	complemented
30	C₇×#488	C₂²	1	12	yes	complemented
31	C₇×#487	C₂²	1	1	yes	characteristic, complemented
32	C₇×#487	C₂²	1	3	yes	complemented
33	C₇×#486	C₂²	1	3	yes	complemented
34	C₇×#486	C₂²	1	12	yes	complemented
35	C₇×#486	C₂²	1	6	yes	complemented
36	C₇×#486	C₂²	1	3	yes	complemented
37	C₇×#418	C₂²	1	12	yes	complemented
38	C₇×#417	C₂²	1	12	yes	complemented
39	C₇×#416	C₂²	1	12	yes	complemented
40	C₂×C₇×#102	C₂²	1	12	yes	complemented
41	C₇×#405	C₂²	1	6	yes	complemented
42	C₄×C₇×M₁₆	C₂²	1	3	yes	complemented
43	C₂×C₄×C₇×C₈	C₂²	1	3	yes	complemented
44	#60622	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₇×H(5,𝔽₂)	—	2	16	no	—
46	C₂×C₇×#41	—	2	2	no	—
47	C₂×C₇×#41	C₂³	1	6	yes	—
48	C₂×C₇×#41	C₂³	1	1	yes	characteristic
49	C₂²×C₇×Q₈	—	2	3	no	—
50	C₂²×C₇×D₄	—	2	6	no	—
51	C₂²×C₇×D₄	—	2	3	no	—
52	C₂²×C₇×D₄	—	2	3	no	—
53	C₂²×C₇×D₄	C₂³	1	6	yes	—
54	C₇×#131	—	2	8	no	—
55	C₂×C₇×M₁₆	C₂³	1	6	yes	—
56	C₂²×C₇×C₈	C₂³	1	6	yes	—
57	C₇×C₄⋊Q₈	—	2	6	no	—
58	C₇×C₄⋊Q₈	—	2	3	no	—
59	C₇×C₄⋊Q₈	—	2	3	no	—
60	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
62	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₇×C₄⋊Q₈	C₂³	1	6	yes	—
64	C₇×#127	—	2	3	no	—
65	C₇×#127	—	2	3	no	—
66	C₇×#127	C₂³	1	3	yes	—
67	C₇×#127	C₂³	1	6	yes	—
68	C₇×#125	—	2	6	no	—
69	C₇×#125	C₂³	1	6	yes	—
70	C₇×#124	C₂³	1	6	yes	—
71	C₇×C₂²⋊Q₈	—	2	3	no	—
72	C₇×C₂²⋊Q₈	—	2	3	no	—
73	C₇×C₂²⋊Q₈	—	2	12	no	—
74	C₇×#121	—	2	3	no	—
75	C₇×#121	—	2	3	no	—
76	C₇×#121	—	2	6	no	—
77	C₇×#121	—	2	6	no	—
78	C₇×#120	—	2	12	no	—
79	C₄×C₇×Q₈	—	2	2	no	—
80	C₄×C₇×Q₈	—	2	3	no	—
81	C₄×C₇×Q₈	—	2	3	no	—
82	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
83	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
84	C₄×C₇×D₄	—	2	6	no	—
85	C₄×C₇×D₄	—	2	3	no	—
86	C₄×C₇×D₄	—	2	3	no	—
87	C₄×C₇×D₄	D₄	1	3	yes	—
88	C₄×C₇×D₄	D₄	1	3	yes	—
89	C₇×#117	C₂³	1	6	yes	—
90	C₇×#117	C₂³	1	3	yes	—
91	C₂×C₇×C₄⋊C₄	—	2	3	no	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
93	C₂×C₄²×C₇	C₂³	1	3	yes	—
94	C₇×#103	C₂³	1	4	yes	—
95	C₇×#103	C₂³	1	12	yes	—
96	C₇×#102	C₂³	1	12	yes	—
97	C₇×#102	C₂³	1	24	yes	—
98	C₇×#102	C₂³	1	12	yes	—
99	C₇×#97	C₂³	1	6	yes	—
100	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₇×C₈	C₂³	1	3	yes	—
102	C₄×C₇×C₈	C₂³	1	6	yes	—
103	#3503	C₂×C₇	1	1	yes	characteristic, complemented
104	#3498	C₂×C₇	1	1	yes	characteristic
105	#3141	C₂×C₇	1	3	yes	complemented
106	#3138	C₂×C₇	1	3	yes	complemented
107	#3136	C₂×C₇	1	12	yes	complemented
108	#3131	C₂×C₇	1	3	yes	complemented
109	C₂×#486	C₂×C₇	1	3	yes	complemented
110	#2897	C₂×C₇	1	4	yes	complemented
111	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
112	C₂⁴×C₇	—	2	6	no	—
113	C₇×#41	—	2	24	no	—
114	C₇×#41	—	4	8	no	—
115	C₇×#41	#41	1	8	yes	—
116	C₂×C₇×Q₈	—	2	1	no	—
117	C₂×C₇×Q₈	—	2	3	no	—
118	C₂×C₇×Q₈	—	2	6	no	—
119	C₂×C₇×Q₈	—	8	6	no	—
120	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
122	C₂×C₇×D₄	—	2	6	no	—
123	C₂×C₇×D₄	—	2	3	no	—
124	C₂×C₇×D₄	—	2	3	no	—
125	C₂×C₇×D₄	—	2	6	no	—
126	C₂×C₇×D₄	—	2	6	no	—
127	C₂×C₇×D₄	—	2	6	no	—
128	C₂×C₇×D₄	—	2	24	no	—
129	C₂×C₇×D₄	—	4	24	no	—
130	C₂×C₇×D₄	—	8	6	no	—
131	C₂×C₇×D₄	—	8	6	no	—
132	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
133	C₂×C₇×D₄	C₂⁴	1	6	yes	—
134	C₂²×C₄×C₇	—	2	6	no	—
135	C₂²×C₄×C₇	—	2	6	no	—
136	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
137	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
138	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
139	C₇×M₁₆	—	2	12	no	—
140	C₂×C₇×C₈	—	2	12	no	—
141	C₂×C₇×C₈	C₂⁴	1	2	yes	—
142	C₂×C₇×C₈	C₂⁴	1	6	yes	—
143	C₇×C₄⋊C₄	—	2	3	no	—
144	C₇×C₄⋊C₄	—	2	6	no	—
145	C₇×C₄⋊C₄	—	2	6	no	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	6	no	—
150	C₇×C₄⋊C₄	—	2	6	no	—
151	C₇×C₄⋊C₄	C₂×D₄	1	3	yes	—
152	C₇×C₄⋊C₄	C₂×D₄	1	3	yes	—
153	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
154	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
155	C₇×C₂²⋊C₄	—	2	6	no	—
156	C₇×C₂²⋊C₄	—	2	6	no	—
157	C₇×C₂²⋊C₄	—	2	6	no	—
158	C₇×C₂²⋊C₄	C₂×D₄	1	6	yes	—
159	C₄²×C₇	—	2	6	no	—
160	C₄²×C₇	C₂×D₄	1	3	yes	—
161	C₄²×C₇	C₂×D₄	1	3	yes	—
162	C₄²×C₇	C₂⁴	1	1	yes	characteristic
163	C₄²×C₇	C₂⁴	1	3	yes	—
164	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
165	C₂×#131	C₂²×C₇	1	2	yes	—
166	Q₈²	—	2	1	no	—
167	#557	—	2	1	no	—
168	#554	—	2	3	no	—
169	#550	—	2	1	no	—
170	#550	—	2	1	no	—
171	D₄×Q₈	—	2	3	no	—
172	D₄²	—	2	3	no	—
173	D₄²	—	2	3	no	—
174	#544	C₂²×C₇	1	6	yes	complemented
175	#535	C₂²×C₇	1	6	yes	—
176	#533	C₂²×C₇	1	3	yes	complemented
177	#532	C₂²×C₇	1	3	yes	—
178	C₂×C₄⋊Q₈	C₂²×C₇	1	3	yes	complemented
179	C₂×#127	C₂²×C₇	1	3	yes	—
180	#520	C₂²×C₇	1	2	yes	—
181	C₄×#41	C₂²×C₇	1	1	yes	characteristic
182	#490	C₂²×C₇	1	12	yes	complemented
183	#489	C₂²×C₇	1	12	yes	complemented
184	#488	C₂²×C₇	1	12	yes	complemented
185	#487	C₂²×C₇	1	1	yes	characteristic, complemented
186	#487	C₂²×C₇	1	3	yes	complemented
187	#486	C₂²×C₇	1	3	yes	complemented
188	#486	C₂²×C₇	1	12	yes	complemented
189	#486	C₂²×C₇	1	6	yes	complemented
190	#486	C₂²×C₇	1	3	yes	complemented
191	#418	C₂²×C₇	1	12	yes	complemented
192	#417	C₂²×C₇	1	12	yes	complemented
193	#416	C₂²×C₇	1	12	yes	complemented
194	C₂×#102	C₂²×C₇	1	12	yes	complemented
195	#405	C₂²×C₇	1	6	yes	complemented
196	C₄×M₁₆	C₂²×C₇	1	3	yes	complemented
197	C₂×C₄×C₈	C₂²×C₇	1	3	yes	complemented
198	C₂³×C₇	—	2	6	no	—
199	C₂³×C₇	—	4	12	no	—
200	C₂³×C₇	—	8	6	no	—
201	C₂³×C₇	—	8	6	no	—
202	C₂³×C₇	C₂²×D₄	1	3	yes	—
203	C₇×Q₈	—	2	4	no	—
204	C₇×Q₈	—	4	6	no	—
205	C₇×Q₈	—	4	2	no	—
206	C₇×Q₈	—	8	6	no	—
207	C₇×Q₈	#124	1	4	yes	—
208	C₇×D₄	—	2	12	no	—
209	C₇×D₄	—	4	12	no	—
210	C₇×D₄	—	4	12	no	—
211	C₇×D₄	—	4	6	no	—
212	C₇×D₄	—	4	6	no	—
213	C₇×D₄	—	8	6	no	—
214	C₇×D₄	—	8	6	no	—
215	C₇×D₄	#124	1	12	yes	—
216	C₂×C₄×C₇	—	2	6	no	—
217	C₂×C₄×C₇	—	2	6	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	6	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	4	12	no	—
222	C₂×C₄×C₇	—	8	6	no	—
223	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
224	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
225	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
226	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂×#41	1	12	yes	—
229	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
230	C₇×C₈	—	2	2	no	—
231	C₇×C₈	—	2	6	no	—
232	H(5,𝔽₂)	—	2	16	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	C₂³×C₇	1	6	yes	—
235	C₂×#41	C₂³×C₇	1	1	yes	characteristic
236	C₂²×Q₈	—	2	3	no	—
237	C₂²×D₄	—	2	6	no	—
238	C₂²×D₄	—	2	3	no	—
239	C₂²×D₄	—	2	3	no	—
240	C₂²×D₄	C₂³×C₇	1	6	yes	—
241	#131	—	2	8	no	—
242	C₂×M₁₆	C₂³×C₇	1	6	yes	—
243	C₂²×C₈	C₂³×C₇	1	6	yes	—
244	C₄⋊Q₈	—	2	6	no	—
245	C₄⋊Q₈	—	2	3	no	—
246	C₄⋊Q₈	—	2	3	no	—
247	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
248	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
249	C₄⋊Q₈	C₂³×C₇	1	6	yes	—
250	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
251	#127	—	2	3	no	—
252	#127	—	2	3	no	—
253	#127	C₂³×C₇	1	3	yes	—
254	#127	C₂³×C₇	1	6	yes	—
255	#125	—	2	6	no	—
256	#125	C₂³×C₇	1	6	yes	—
257	#124	C₂³×C₇	1	6	yes	—
258	C₂²⋊Q₈	—	2	3	no	—
259	C₂²⋊Q₈	—	2	3	no	—
260	C₂²⋊Q₈	—	2	12	no	—
261	#121	—	2	3	no	—
262	#121	—	2	3	no	—
263	#121	—	2	6	no	—
264	#121	—	2	6	no	—
265	#120	—	2	12	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	3	no	—
268	C₄×Q₈	—	2	3	no	—
269	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
270	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
271	C₄×D₄	—	2	6	no	—
272	C₄×D₄	—	2	3	no	—
273	C₄×D₄	—	2	3	no	—
274	C₄×D₄	C₇×D₄	1	3	yes	—
275	C₄×D₄	C₇×D₄	1	3	yes	—
276	#117	C₂³×C₇	1	6	yes	—
277	#117	C₂³×C₇	1	3	yes	—
278	C₂×C₄⋊C₄	—	2	3	no	—
279	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
280	C₂×C₄²	C₂³×C₇	1	3	yes	—
281	#103	C₂³×C₇	1	4	yes	—
282	#103	C₂³×C₇	1	12	yes	—
283	#102	C₂³×C₇	1	12	yes	—
284	#102	C₂³×C₇	1	24	yes	—
285	#102	C₂³×C₇	1	12	yes	—
286	#97	C₂³×C₇	1	6	yes	—
287	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₇	1	3	yes	—
289	C₄×C₈	C₂³×C₇	1	6	yes	—
290	C₂²×C₇	—	2	3	no	—
291	C₂²×C₇	—	2	3	no	—
292	C₂²×C₇	—	4	6	no	—
293	C₂²×C₇	—	4	6	no	—
294	C₂²×C₇	—	4	6	no	—
295	C₂²×C₇	—	16	12	no	—
296	C₂²×C₇	C₂×#124	1	6	yes	—
297	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
298	C₄×C₇	—	2	3	no	—
299	C₄×C₇	—	2	3	no	—
300	C₄×C₇	—	4	2	no	—
301	C₄×C₇	—	4	6	no	—
302	C₄×C₇	—	4	2	no	—
303	C₄×C₇	C₂×#124	1	6	yes	—
304	C₄×C₇	#576	1	2	yes	—
305	C₄×C₇	#577	1	2	yes	—
306	C₄×C₇	C₂²×#41	1	2	yes	—
307	C₂⁴	—	2	6	no	—
308	#41	—	2	24	no	—
309	#41	—	4	8	no	—
310	#41	C₇×#41	1	8	yes	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	3	no	—
313	C₂×Q₈	—	2	6	no	—
314	C₂×Q₈	—	8	6	no	—
315	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
316	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
317	C₂×D₄	—	2	6	no	—
318	C₂×D₄	—	2	3	no	—
319	C₂×D₄	—	2	3	no	—
320	C₂×D₄	—	2	6	no	—
321	C₂×D₄	—	2	6	no	—
322	C₂×D₄	—	2	6	no	—
323	C₂×D₄	—	2	24	no	—
324	C₂×D₄	—	4	24	no	—
325	C₂×D₄	—	8	6	no	—
326	C₂×D₄	—	8	6	no	—
327	C₂×D₄	C₂×C₇×D₄	1	3	yes	—
328	C₂×D₄	C₂⁴×C₇	1	6	yes	—
329	C₂²×C₄	—	2	6	no	—
330	C₂²×C₄	—	2	6	no	—
331	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
332	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
333	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
334	M₁₆	—	2	12	no	—
335	C₂×C₈	—	2	12	no	—
336	C₂×C₈	C₂⁴×C₇	1	2	yes	—
337	C₂×C₈	C₂⁴×C₇	1	6	yes	—
338	C₄⋊C₄	—	2	3	no	—
339	C₄⋊C₄	—	2	6	no	—
340	C₄⋊C₄	—	2	6	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	6	no	—
345	C₄⋊C₄	—	2	6	no	—
346	C₄⋊C₄	C₂×C₇×D₄	1	3	yes	—
347	C₄⋊C₄	C₂×C₇×D₄	1	3	yes	—
348	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
349	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
350	C₂²⋊C₄	—	2	6	no	—
351	C₂²⋊C₄	—	2	6	no	—
352	C₂²⋊C₄	—	2	6	no	—
353	C₂²⋊C₄	C₂×C₇×D₄	1	6	yes	—
354	C₄²	—	2	6	no	—
355	C₄²	C₂×C₇×D₄	1	3	yes	—
356	C₄²	C₂×C₇×D₄	1	3	yes	—
357	C₄²	C₂⁴×C₇	1	1	yes	characteristic
358	C₄²	C₂⁴×C₇	1	3	yes	—
359	C₂×C₇	—	2	6	no	—
360	C₂×C₇	—	8	6	no	—
361	C₂×C₇	C₂²×#124	1	1	yes	characteristic
362	C₂×C₇	C₂×#576	1	1	yes	characteristic
363	C₂×C₇	C₂×#577	1	1	yes	characteristic
364	C₂³	—	2	6	no	—
365	C₂³	—	4	12	no	—
366	C₂³	—	8	6	no	—
367	C₂³	—	8	6	no	—
368	C₂³	C₂²×C₇×D₄	1	3	yes	—
369	Q₈	—	2	4	no	—
370	Q₈	—	4	6	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	6	no	—
373	Q₈	C₇×#124	1	4	yes	—
374	D₄	—	2	12	no	—
375	D₄	—	4	12	no	—
376	D₄	—	4	12	no	—
377	D₄	—	4	6	no	—
378	D₄	—	4	6	no	—
379	D₄	—	8	6	no	—
380	D₄	—	8	6	no	—
381	D₄	C₇×#124	1	12	yes	—
382	C₂×C₄	—	2	6	no	—
383	C₂×C₄	—	2	6	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	6	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	12	no	—
388	C₂×C₄	—	8	6	no	—
389	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
390	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
391	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
392	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₇×#41	1	12	yes	—
395	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	6	no	—
398	C₇	#60622	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	4	6	no	—
402	C₂²	—	4	6	no	—
403	C₂²	—	4	6	no	—
404	C₂²	—	16	12	no	—
405	C₂²	C₂×C₇×#124	1	6	yes	—
406	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
407	C₄	—	2	3	no	—
408	C₄	—	2	3	no	—
409	C₄	—	4	6	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	C₂×C₇×#124	1	6	yes	—
413	C₄	C₇×#576	1	2	yes	—
414	C₄	C₇×#577	1	2	yes	—
415	C₄	C₂²×C₇×#41	1	2	yes	—
416	C₂	—	2	6	no	—
417	C₂	—	8	6	no	—
418	C₂	C₂²×C₇×#124	1	1	yes	characteristic
419	C₂	C₂×C₇×#576	1	1	yes	characteristic
420	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3503	C₂	semidirect
3. C₇×#3141	C₂	semidirect
4. C₇×#3138	C₂	semidirect
5. C₇×#3136	C₂	semidirect
6. C₇×#3131	C₂	semidirect
7. C₂×C₇×#486	C₂	semidirect
8. C₇×#2897	C₂	semidirect
9. C₄×C₇×#131	C₂	semidirect
20. C₇×#544	C₂²	semidirect
22. C₇×#533	C₂²	semidirect
24. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
28. C₇×#490	C₂²	semidirect
29. C₇×#489	C₂²	semidirect
30. C₇×#488	C₂²	semidirect
31. C₇×#487	C₂²	semidirect
32. C₇×#487	C₂²	semidirect
33. C₇×#486	C₂²	semidirect
34. C₇×#486	C₂²	semidirect
35. C₇×#486	C₂²	semidirect
36. C₇×#486	C₂²	semidirect
37. C₇×#418	C₂²	semidirect
38. C₇×#417	C₂²	semidirect
39. C₇×#416	C₂²	semidirect
40. C₂×C₇×#102	C₂²	semidirect
41. C₇×#405	C₂²	semidirect
42. C₄×C₇×M₁₆	C₂²	semidirect
43. C₂×C₄×C₇×C₈	C₂²	semidirect
44. #60622	C₇	direct (N × H)
103. #3503	C₂×C₇	semidirect
105. #3141	C₂×C₇	semidirect
106. #3138	C₂×C₇	semidirect
107. #3136	C₂×C₇	semidirect
108. #3131	C₂×C₇	semidirect
109. C₂×#486	C₂×C₇	semidirect
110. #2897	C₂×C₇	semidirect
111. C₄×#131	C₂×C₇	semidirect
174. #544	C₂²×C₇	semidirect
176. #533	C₂²×C₇	semidirect
178. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
182. #490	C₂²×C₇	semidirect
183. #489	C₂²×C₇	semidirect
184. #488	C₂²×C₇	semidirect
185. #487	C₂²×C₇	semidirect
186. #487	C₂²×C₇	semidirect
187. #486	C₂²×C₇	semidirect
188. #486	C₂²×C₇	semidirect
189. #486	C₂²×C₇	semidirect
190. #486	C₂²×C₇	semidirect
191. #418	C₂²×C₇	semidirect
192. #417	C₂²×C₇	semidirect
193. #416	C₂²×C₇	semidirect
194. C₂×#102	C₂²×C₇	semidirect
195. #405	C₂²×C₇	semidirect
196. C₄×M₁₆	C₂²×C₇	semidirect
197. C₂×C₄×C₈	C₂²×C₇	semidirect
398. C₇	#60622	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×#3503	2
C₇×#3498	2
C₇×#3141	2
C₇×#3138	2
C₇×#3136	2
C₇×#3131	2
C₂×C₇×#486	2
C₇×#2897	2
C₄×C₇×#131	2
#60622	7

Subgroups — C7×#60622 #13237838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60622 #13237838