Subgroups — C₇×#17832 #13195048

Order 1792.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2965	C₂	1	1	yes	maximal, characteristic
2	C₇×#2925	C₂	1	1	yes	maximal, characteristic
3	C₇×#2906	C₂	1	1	yes	maximal, characteristic
4	C₇×#1574	C₂	1	2	yes	maximal, complemented
5	C₇×#1573	C₂	1	2	yes	maximal, complemented
6	C₇×#1571	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1569	C₂	1	2	yes	maximal, complemented
9	C₇×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1565	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#131	—	2	1	no	—
13	C₄×C₇×#41	C₂²	1	1	yes	characteristic
14	C₇×#446	C₄	1	1	yes	characteristic
15	C₇×#446	C₄	1	1	yes	characteristic
16	C₇×#436	C₄	1	1	yes	characteristic
17	C₇×#436	C₄	1	1	yes	characteristic
18	C₇×#435	C₄	1	2	yes	—
19	C₇×#435	C₄	1	2	yes	—
20	C₇×#433	—	2	2	no	—
21	C₇×#432	C₂²	1	2	yes	—
22	C₇×#431	C₂²	1	2	yes	—
23	C₇×#431	C₂²	1	1	yes	characteristic
24	C₇×#431	C₂²	1	2	yes	—
25	C₇×#424	—	2	1	no	—
26	C₇×#424	—	2	2	no	—
27	C₇×#423	C₂²	1	1	yes	characteristic
28	C₇×#423	C₂²	1	2	yes	—
29	C₇×#423	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₇×#408	—	2	1	no	—
34	C₇×#405	—	2	1	no	—
35	C₄×C₇×M₁₆	C₂²	1	2	yes	—
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×#335	C₂²	1	1	yes	characteristic
40	C₇×#335	C₂²	1	1	yes	characteristic
41	C₇×#335	C₂²	1	2	yes	—
42	C₇×#335	C₂²	1	2	yes	—
43	C₇×#334	C₂²	1	2	yes	—
44	C₇×#334	C₂²	1	2	yes	—
45	C₇×#334	C₂²	1	2	yes	—
46	C₇×#334	C₂²	1	2	yes	—
47	#17832	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	D₄	1	1	yes	characteristic
49	C₇×#131	—	4	4	no	—
50	C₂×C₇×M₁₆	—	2	1	no	—
51	C₂×C₇×M₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	—	2	1	no	—
53	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
55	C₂²×C₇×C₈	—	2	1	no	—
56	C₂²×C₇×C₈	—	2	2	no	—
57	C₂²×C₇×C₈	—	2	1	no	—
58	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
60	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₄×C₇×Q₈	Q₈	1	1	yes	characteristic
62	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
63	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
64	C₄×C₇×D₄	Q₈	1	2	yes	—
65	C₄×C₇×D₄	Q₈	1	1	yes	characteristic
66	C₇×#117	D₄	1	1	yes	characteristic
67	C₇×#117	D₄	1	2	yes	—
68	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	2	yes	—
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	—	2	1	no	—
72	C₇×C₄⋊C₈	—	2	1	no	—
73	C₇×C₄⋊C₈	—	2	2	no	—
74	C₇×C₄⋊C₈	—	2	1	no	—
75	C₇×C₄⋊C₈	—	2	1	no	—
76	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
77	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
78	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₇×C₄⋊C₈	C₂³	1	2	yes	—
81	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₇×C₄⋊C₈	C₂³	1	2	yes	—
83	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₇×C₂²⋊C₈	—	2	2	no	—
87	C₇×C₂²⋊C₈	—	2	2	no	—
88	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
89	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
90	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
91	C₇×#97	—	2	2	no	—
92	C₇×#97	C₂×C₄	1	2	yes	—
93	C₇×#97	C₂×C₄	1	2	yes	—
94	C₄×C₇×C₈	—	2	2	no	—
95	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
97	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
98	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
99	C₄×C₇×C₈	C₂³	1	2	yes	—
100	#2965	C₂×C₇	1	1	yes	characteristic
101	#2925	C₂×C₇	1	1	yes	characteristic
102	#2906	C₂×C₇	1	1	yes	characteristic
103	#1574	C₂×C₇	1	2	yes	complemented
104	#1573	C₂×C₇	1	2	yes	complemented
105	#1571	C₂×C₇	1	1	yes	characteristic, complemented
106	#1570	C₂×C₇	1	1	yes	characteristic, complemented
107	#1569	C₂×C₇	1	2	yes	complemented
108	#1566	C₂×C₇	1	1	yes	characteristic, complemented
109	#1565	C₂×C₇	1	2	yes	complemented
110	C₂×#335	C₂×C₇	1	1	yes	characteristic, complemented
111	C₇×#41	—	2	2	no	—
112	C₇×#41	—	2	2	no	—
113	C₂×C₇×Q₈	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₇×D₄	C₄⋊C₄	1	2	yes	—
115	C₂×C₇×D₄	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
121	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
122	C₇×M₁₆	—	2	4	no	—
123	C₇×M₁₆	—	4	2	no	—
124	C₇×M₁₆	—	4	4	no	—
125	C₇×M₁₆	—	4	2	no	—
126	C₇×M₁₆	—	4	2	no	—
127	C₂×C₇×C₈	—	2	2	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	4	1	no	—
135	C₂×C₇×C₈	—	4	4	no	—
136	C₂×C₇×C₈	—	4	2	no	—
137	C₂×C₇×C₈	—	4	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	2	yes	—
142	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
144	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
145	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
146	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
147	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
148	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
149	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
150	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
151	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₇	C₂²×C₄	1	2	yes	—
153	C₄²×C₇	C₂×D₄	1	2	yes	—
154	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇	C₂×Q₈	1	2	yes	—
156	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
157	C₄²×C₇	C₂⁴	1	1	yes	characteristic
158	C₂×#131	—	2	1	no	—
159	C₄×#41	C₂²×C₇	1	1	yes	characteristic
160	#446	C₄×C₇	1	1	yes	characteristic
161	#446	C₄×C₇	1	1	yes	characteristic
162	#436	C₄×C₇	1	1	yes	characteristic
163	#436	C₄×C₇	1	1	yes	characteristic
164	#435	C₄×C₇	1	2	yes	—
165	#435	C₄×C₇	1	2	yes	—
166	#433	—	2	2	no	—
167	#432	C₂²×C₇	1	2	yes	—
168	#431	C₂²×C₇	1	2	yes	—
169	#431	C₂²×C₇	1	1	yes	characteristic
170	#431	C₂²×C₇	1	2	yes	—
171	#424	—	2	1	no	—
172	#424	—	2	2	no	—
173	#423	C₂²×C₇	1	1	yes	characteristic
174	#423	C₂²×C₇	1	1	yes	characteristic
175	#423	C₂²×C₇	1	2	yes	—
176	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
179	#408	—	2	1	no	—
180	#405	—	2	1	no	—
181	C₄×M₁₆	C₂²×C₇	1	2	yes	—
182	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
183	#335	C₂²×C₇	1	1	yes	characteristic
184	#335	C₂²×C₇	1	1	yes	characteristic
185	#335	C₂²×C₇	1	1	yes	characteristic
186	#335	C₂²×C₇	1	1	yes	characteristic
187	#335	C₂²×C₇	1	2	yes	—
188	#335	C₂²×C₇	1	2	yes	—
189	#334	C₂²×C₇	1	2	yes	—
190	#334	C₂²×C₇	1	2	yes	—
191	#334	C₂²×C₇	1	2	yes	—
192	#334	C₂²×C₇	1	2	yes	—
193	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
194	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₇×Q₈	—	2	2	no	—
196	C₇×D₄	—	2	4	no	—
197	C₇×D₄	—	2	2	no	—
198	C₂×C₄×C₇	—	2	1	no	—
199	C₂×C₄×C₇	—	2	2	no	—
200	C₂×C₄×C₇	—	2	1	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	4	1	no	—
205	C₂×C₄×C₇	—	4	2	no	—
206	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
208	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
209	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
210	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
213	C₂×C₄×C₇	#137	1	2	yes	—
214	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
217	C₇×C₈	—	2	1	no	—
218	C₇×C₈	—	2	2	no	—
219	C₇×C₈	—	2	1	no	—
220	C₇×C₈	—	2	1	no	—
221	C₇×C₈	—	2	2	no	—
222	C₇×C₈	—	4	1	no	—
223	C₇×C₈	—	4	1	no	—
224	C₇×C₈	—	4	1	no	—
225	C₇×C₈	—	4	2	no	—
226	C₇×C₈	—	4	1	no	—
227	C₇×C₈	—	4	2	no	—
228	C₇×C₈	#131	1	2	yes	complemented
229	C₂×#41	C₇×D₄	1	1	yes	characteristic
230	#131	—	4	4	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
235	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	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	C₇×Q₈	1	1	yes	characteristic
243	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
244	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
245	C₄×D₄	C₇×Q₈	1	2	yes	—
246	C₄×D₄	C₇×Q₈	1	1	yes	characteristic
247	#117	C₇×D₄	1	1	yes	characteristic
248	#117	C₇×D₄	1	2	yes	—
249	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₇	1	2	yes	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
258	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
259	C₄⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
260	C₄⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
261	C₄⋊C₈	C₂³×C₇	1	2	yes	—
262	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
263	C₄⋊C₈	C₂³×C₇	1	2	yes	—
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	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
270	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
271	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
272	#97	—	2	2	no	—
273	#97	C₂×C₄×C₇	1	2	yes	—
274	#97	C₂×C₄×C₇	1	2	yes	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
277	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₇	1	2	yes	—
281	C₂²×C₇	—	2	1	no	—
282	C₂²×C₇	—	2	1	no	—
283	C₂²×C₇	—	2	2	no	—
284	C₂²×C₇	—	2	2	no	—
285	C₂²×C₇	—	2	2	no	—
286	C₂²×C₇	#428	1	2	yes	—
287	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
288	C₄×C₇	—	2	1	no	—
289	C₄×C₇	—	2	2	no	—
290	C₄×C₇	—	2	2	no	—
291	C₄×C₇	—	2	1	no	—
292	C₄×C₇	—	2	1	no	—
293	C₄×C₇	—	2	2	no	—
294	C₄×C₇	#428	1	2	yes	—
295	C₄×C₇	C₂×#131	1	1	yes	characteristic
296	C₄×C₇	#568	1	1	yes	characteristic
297	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
298	C₄×C₇	C₂×#137	1	1	yes	characteristic
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	C₂×Q₈	C₇×C₄⋊C₄	1	1	yes	characteristic
302	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
303	C₂×D₄	C₇×C₄⋊C₄	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
306	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
307	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
309	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
310	M₁₆	—	2	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	—	4	4	no	—
313	M₁₆	—	4	2	no	—
314	M₁₆	—	4	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	4	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
327	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
328	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
329	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
330	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
331	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
332	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
333	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
334	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
335	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
336	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
337	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
338	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
339	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
340	C₄²	C₂²×C₄×C₇	1	2	yes	—
341	C₄²	C₂×C₇×D₄	1	2	yes	—
342	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
343	C₄²	C₂×C₇×Q₈	1	2	yes	—
344	C₄²	C₂×C₇×Q₈	1	1	yes	characteristic
345	C₄²	C₂⁴×C₇	1	1	yes	characteristic
346	C₂×C₇	—	2	2	no	—
347	C₂×C₇	—	4	2	no	—
348	C₂×C₇	#2906	1	1	yes	characteristic
349	C₂×C₇	C₂×#428	1	1	yes	characteristic
350	C₂×C₇	#2916	1	1	yes	characteristic
351	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
352	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
353	Q₈	—	2	2	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
366	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
367	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
368	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
369	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
371	C₂×C₄	C₇×#137	1	2	yes	—
372	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	2	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	2	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	1	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	2	no	—
386	C₈	C₇×#131	1	2	yes	complemented
387	C₇	#17832	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	C₇×#428	1	2	yes	—
394	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	C₇×#428	1	2	yes	—
402	C₄	C₂×C₇×#131	1	1	yes	characteristic
403	C₄	C₇×#568	1	1	yes	characteristic
404	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₄	C₂×C₇×#137	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	C₇×#2906	1	1	yes	characteristic
409	C₂	C₂×C₇×#428	1	1	yes	characteristic
410	C₂	C₇×#2916	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	C₂²×C₄⋊C₄
prime radical	C₂×C₇×#41	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×#1574	C₂	semidirect
5. C₇×#1573	C₂	semidirect
6. C₇×#1571	C₂	semidirect
7. C₇×#1570	C₂	semidirect
8. C₇×#1569	C₂	semidirect
9. C₇×#1566	C₂	semidirect
10. C₇×#1565	C₂	semidirect
11. C₂×C₇×#335	C₂	semidirect
47. #17832	C₇	direct (N × H)
103. #1574	C₂×C₇	semidirect
104. #1573	C₂×C₇	semidirect
105. #1571	C₂×C₇	semidirect
106. #1570	C₂×C₇	semidirect
107. #1569	C₂×C₇	semidirect
108. #1566	C₂×C₇	semidirect
109. #1565	C₂×C₇	semidirect
110. C₂×#335	C₂×C₇	semidirect
228. C₇×C₈	#131	semidirect
386. C₈	C₇×#131	semidirect
387. C₇	#17832	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×#2965	2
C₇×#2925	2
C₇×#2906	2
C₇×#1574	2
C₇×#1573	2
C₇×#1571	2
C₇×#1570	2
C₇×#1569	2
C₇×#1566	2
C₇×#1565	2
C₂×C₇×#335	2
#17832	7

Subgroups — C7×#17832 #13195048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17832 #13195048