Subgroups — C₇×#18089 #13195305

Order 1792.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3167	C₂	1	1	yes	maximal, characteristic
2	C₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2979	C₂	1	1	yes	maximal, characteristic
4	C₇×#1592	C₂	1	2	yes	maximal, complemented
5	C₇×#1583	C₂	1	2	yes	maximal, complemented
6	C₇×#1582	C₂	1	2	yes	maximal, complemented
7	C₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1485	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1484	C₂	1	1	yes	maximal, characteristic
11	C₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#533	C₂²	1	1	yes	characteristic
13	C₇×#532	C₂²	1	1	yes	characteristic
14	C₇×#498	C₄	1	1	yes	characteristic
15	C₇×#492	C₄	1	1	yes	characteristic
16	C₇×#487	C₄	1	1	yes	characteristic
17	C₇×#486	C₄	1	1	yes	characteristic
18	C₇×#465	C₄	1	2	yes	—
19	C₇×#465	C₄	1	2	yes	—
20	C₇×#446	—	2	1	no	—
21	C₇×#446	C₂²	1	2	yes	—
22	C₇×C₈×Q₈	—	2	1	no	—
23	C₇×C₈×Q₈	C₂²	1	2	yes	—
24	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
25	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
26	C₇×#436	—	2	1	no	—
27	C₇×#436	C₂²	1	2	yes	—
28	C₇×C₈×D₄	—	2	1	no	—
29	C₇×C₈×D₄	C₂²	1	2	yes	—
30	C₇×#433	—	2	2	no	—
31	C₇×#431	C₂²	1	1	yes	characteristic
32	C₇×#431	C₂²	1	1	yes	characteristic
33	C₇×#431	C₂²	1	1	yes	characteristic
34	C₇×#408	—	2	2	no	—
35	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
37	C₇×#335	C₂²	1	1	yes	characteristic
38	C₇×#335	C₂²	1	1	yes	characteristic
39	C₇×#334	C₂²	1	1	yes	characteristic
40	C₇×#334	C₂²	1	1	yes	characteristic
41	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₇×D₄⋊C₈	C₂²	1	2	yes	—
44	C₇×D₄⋊C₈	C₂²	1	2	yes	—
45	C₇×#322	C₂²	1	2	yes	—
46	C₇×#322	C₂²	1	2	yes	—
47	#18089	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	1	no	—
49	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₇×M₁₆	—	2	1	no	—
52	C₂×C₇×M₁₆	—	2	2	no	—
53	C₂²×C₇×C₈	—	2	2	no	—
54	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
56	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
59	C₇×#127	C₂×C₄	1	1	yes	characteristic
60	C₇×#125	—	2	1	no	—
61	C₇×#124	—	2	1	no	—
62	C₇×C₂²⋊Q₈	—	2	1	no	—
63	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
64	C₇×#121	—	2	1	no	—
65	C₇×#121	C₂×C₄	1	2	yes	—
66	C₄×C₇×Q₈	—	2	1	no	—
67	C₄×C₇×Q₈	C₂³	1	2	yes	—
68	C₄×C₇×D₄	—	2	1	no	—
69	C₄×C₇×D₄	C₂³	1	2	yes	—
70	C₇×#117	—	2	1	no	—
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×#106	C₂×C₄	1	2	yes	—
73	C₇×#106	C₂×C₄	1	2	yes	—
74	C₇×C₄⋊C₈	—	2	2	no	—
75	C₇×C₄⋊C₈	—	2	2	no	—
76	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
77	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
78	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₇×#103	C₂×C₄	1	2	yes	—
83	C₇×#103	C₂×C₄	1	2	yes	—
84	C₇×#102	C₂×C₄	1	2	yes	—
85	C₇×#102	C₂×C₄	1	2	yes	—
86	C₇×C₂²⋊C₈	—	2	1	no	—
87	C₇×C₂²⋊C₈	—	2	1	no	—
88	C₇×C₂²⋊C₈	—	2	2	no	—
89	C₇×C₂²⋊C₈	—	2	2	no	—
90	C₇×C₂²⋊C₈	D₄	1	2	yes	—
91	C₇×#97	—	2	2	no	—
92	C₇×#97	—	2	1	no	—
93	C₄×C₇×C₈	—	2	2	no	—
94	C₄×C₇×C₈	—	2	1	no	—
95	C₄×C₇×C₈	—	2	1	no	—
96	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
97	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₇×C₈	C₂³	1	2	yes	—
99	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₇×C₈	C₂³	1	2	yes	—
102	#3167	C₂×C₇	1	1	yes	characteristic
103	#2986	C₂×C₇	1	1	yes	characteristic, complemented
104	#2979	C₂×C₇	1	1	yes	characteristic
105	#1592	C₂×C₇	1	2	yes	complemented
106	#1583	C₂×C₇	1	2	yes	complemented
107	#1582	C₂×C₇	1	2	yes	complemented
108	SD₁₆⋊C₈	C₂×C₇	1	2	yes	complemented
109	#1564	C₂×C₇	1	1	yes	characteristic, complemented
110	#1485	C₂×C₇	1	1	yes	characteristic, complemented
111	#1484	C₂×C₇	1	1	yes	characteristic
112	#1451	C₂×C₇	1	1	yes	characteristic, complemented
113	C₇×#41	—	8	1	no	—
114	C₇×#41	—	8	1	no	—
115	C₂×C₇×Q₈	—	2	1	no	—
116	C₂×C₇×Q₈	—	2	1	no	—
117	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
118	C₂×C₇×D₄	—	2	2	no	—
119	C₂×C₇×D₄	—	2	1	no	—
120	C₂×C₇×D₄	—	2	1	no	—
121	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	#41	1	1	yes	characteristic
126	C₇×SD₁₆	—	2	4	no	—
127	C₇×SD₁₆	—	4	2	no	—
128	C₇×M₁₆	—	4	2	no	—
129	C₇×M₁₆	—	8	2	no	—
130	C₂×C₇×C₈	—	2	2	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	1	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	2	no	—
136	C₂×C₇×C₈	—	4	1	no	—
137	C₂×C₇×C₈	—	8	2	no	—
138	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
143	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
144	C₇×C₄⋊C₄	—	2	1	no	—
145	C₇×C₄⋊C₄	—	2	1	no	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	2	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
151	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
152	C₇×C₂²⋊C₄	—	2	2	no	—
153	C₇×C₂²⋊C₄	—	2	2	no	—
154	C₇×C₂²⋊C₄	—	2	2	no	—
155	C₄²×C₇	—	2	2	no	—
156	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₇	#41	1	1	yes	characteristic
159	C₄²×C₇	C₂⁴	1	1	yes	characteristic
160	#533	C₂²×C₇	1	1	yes	characteristic
161	#532	C₂²×C₇	1	1	yes	characteristic
162	#498	C₄×C₇	1	1	yes	characteristic
163	#492	C₄×C₇	1	1	yes	characteristic
164	#487	C₄×C₇	1	1	yes	characteristic
165	#486	C₄×C₇	1	1	yes	characteristic
166	#465	C₄×C₇	1	2	yes	—
167	#465	C₄×C₇	1	2	yes	—
168	#446	—	2	1	no	—
169	#446	C₂²×C₇	1	2	yes	—
170	C₈×Q₈	—	2	1	no	—
171	C₈×Q₈	C₂²×C₇	1	2	yes	—
172	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
173	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
174	#436	—	2	1	no	—
175	#436	C₂²×C₇	1	2	yes	—
176	C₈×D₄	—	2	1	no	—
177	C₈×D₄	C₂²×C₇	1	2	yes	—
178	#433	—	2	2	no	—
179	#431	C₂²×C₇	1	1	yes	characteristic
180	#431	C₂²×C₇	1	1	yes	characteristic
181	#431	C₂²×C₇	1	1	yes	characteristic
182	#408	—	2	2	no	—
183	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
185	#335	C₂²×C₇	1	1	yes	characteristic
186	#335	C₂²×C₇	1	1	yes	characteristic
187	#334	C₂²×C₇	1	1	yes	characteristic
188	#334	C₂²×C₇	1	1	yes	characteristic
189	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
190	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
191	D₄⋊C₈	C₂²×C₇	1	2	yes	—
192	D₄⋊C₈	C₂²×C₇	1	2	yes	—
193	#322	C₂²×C₇	1	2	yes	—
194	#322	C₂²×C₇	1	2	yes	—
195	C₂³×C₇	—	2	2	no	—
196	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
197	C₇×Q₈	—	2	2	no	—
198	C₇×Q₈	—	2	2	no	—
199	C₇×Q₈	—	4	2	no	—
200	C₇×Q₈	—	8	1	no	—
201	C₇×D₄	—	2	2	no	—
202	C₇×D₄	—	2	2	no	—
203	C₇×D₄	—	4	2	no	—
204	C₇×D₄	—	8	1	no	—
205	C₇×D₄	—	8	2	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	4	2	no	—
215	C₂×C₄×C₇	—	4	2	no	—
216	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
222	C₇×C₈	—	2	1	no	—
223	C₇×C₈	—	2	1	no	—
224	C₇×C₈	—	2	1	no	—
225	C₇×C₈	—	2	2	no	—
226	C₇×C₈	—	2	2	no	—
227	C₇×C₈	—	4	2	no	—
228	C₇×C₈	—	4	1	no	—
229	C₇×C₈	—	4	1	no	—
230	C₇×C₈	—	4	1	no	—
231	C₇×C₈	—	4	1	no	—
232	C₇×C₈	#131	1	2	yes	—
233	C₂×#41	—	2	1	no	—
234	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
235	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
240	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
241	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
242	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
243	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
244	#127	C₂×C₄×C₇	1	1	yes	characteristic
245	#125	—	2	1	no	—
246	#124	—	2	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
249	#121	—	2	1	no	—
250	#121	C₂×C₄×C₇	1	2	yes	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	C₂³×C₇	1	2	yes	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	C₂³×C₇	1	2	yes	—
255	#117	—	2	1	no	—
256	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
257	#106	C₂×C₄×C₇	1	2	yes	—
258	#106	C₂×C₄×C₇	1	2	yes	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
262	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
263	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
264	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
265	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
266	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
267	#103	C₂×C₄×C₇	1	2	yes	—
268	#103	C₂×C₄×C₇	1	2	yes	—
269	#102	C₂×C₄×C₇	1	2	yes	—
270	#102	C₂×C₄×C₇	1	2	yes	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	C₇×D₄	1	2	yes	—
276	#97	—	2	2	no	—
277	#97	—	2	1	no	—
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
282	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₇	1	2	yes	—
284	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₇	1	2	yes	—
287	C₂²×C₇	—	2	1	no	—
288	C₂²×C₇	—	2	1	no	—
289	C₂²×C₇	—	2	1	no	—
290	C₂²×C₇	—	4	2	no	—
291	C₂²×C₇	—	4	2	no	—
292	C₂²×C₇	—	4	2	no	—
293	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₇	—	2	1	no	—
295	C₄×C₇	—	2	1	no	—
296	C₄×C₇	—	2	1	no	—
297	C₄×C₇	—	4	2	no	—
298	C₄×C₇	—	4	2	no	—
299	C₄×C₇	—	4	2	no	—
300	C₄×C₇	#444	1	2	yes	—
301	C₄×C₇	C₂×#131	1	1	yes	characteristic
302	C₄×C₇	#568	1	1	yes	characteristic
303	C₄×C₇	#577	1	1	yes	characteristic
304	C₄×C₇	#577	1	1	yes	characteristic
305	#41	—	8	1	no	—
306	#41	—	8	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₇×#41	1	1	yes	characteristic
318	SD₁₆	—	2	4	no	—
319	SD₁₆	—	4	2	no	—
320	M₁₆	—	4	2	no	—
321	M₁₆	—	8	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	8	2	no	—
330	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
331	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
332	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
333	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
335	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
343	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
349	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
350	C₄²	C₇×#41	1	1	yes	characteristic
351	C₄²	C₂⁴×C₇	1	1	yes	characteristic
352	C₂×C₇	—	4	1	no	—
353	C₂×C₇	—	8	2	no	—
354	C₂×C₇	#2935	1	1	yes	characteristic
355	C₂×C₇	#2949	1	1	yes	characteristic
356	C₂×C₇	C₂×#444	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	8	1	no	—
363	D₄	—	2	2	no	—
364	D₄	—	2	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	8	1	no	—
367	D₄	—	8	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
379	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
380	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
381	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
383	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
384	C₈	—	2	1	no	—
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	C₇×#131	1	2	yes	—
395	C₇	#18089	1	1	yes	characteristic, direct product factor, Sylow
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	C₇×#444	1	2	yes	—
410	C₄	C₂×C₇×#131	1	1	yes	characteristic
411	C₄	C₇×#568	1	1	yes	characteristic
412	C₄	C₇×#577	1	1	yes	characteristic
413	C₄	C₇×#577	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	8	2	no	—
416	C₂	C₇×#2935	1	1	yes	characteristic
417	C₂	C₇×#2949	1	1	yes	characteristic
418	C₂	C₂×C₇×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2986	C₂	semidirect
4. C₇×#1592	C₂	semidirect
5. C₇×#1583	C₂	semidirect
6. C₇×#1582	C₂	semidirect
7. C₇×SD₁₆⋊C₈	C₂	semidirect
8. C₇×#1564	C₂	semidirect
9. C₇×#1485	C₂	semidirect
11. C₇×#1451	C₂	semidirect
47. #18089	C₇	direct (N × H)
103. #2986	C₂×C₇	semidirect
105. #1592	C₂×C₇	semidirect
106. #1583	C₂×C₇	semidirect
107. #1582	C₂×C₇	semidirect
108. SD₁₆⋊C₈	C₂×C₇	semidirect
109. #1564	C₂×C₇	semidirect
110. #1485	C₂×C₇	semidirect
112. #1451	C₂×C₇	semidirect
395. C₇	#18089	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×#3167	2
C₇×#2986	2
C₇×#2979	2
C₇×#1592	2
C₇×#1583	2
C₇×#1582	2
C₇×SD₁₆⋊C₈	2
C₇×#1564	2
C₇×#1485	2
C₇×#1484	2
C₇×#1451	2
#18089	7

Subgroups — C7×#18089 #13195305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#18089 #13195305