Subgroups — C₇×#23150 #13200366

Order 1792.

780 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₇×#1984	C₂	1	1	yes	maximal, characteristic
5	C₇×#1984	C₂	1	1	yes	maximal, characteristic
6	C₇×#1940	C₂	1	2	yes	maximal
7	C₇×#1917	C₂	1	2	yes	maximal
8	C₇×#1916	C₂	1	2	yes	maximal
9	C₇×#1771	C₂	1	2	yes	maximal
10	C₇×#1767	C₂	1	1	yes	maximal, characteristic
11	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₇×#446	—	2	4	no	—
16	C₇×C₈×Q₈	—	2	4	no	—
17	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#97	C₂²	1	2	yes	—
24	C₂×C₇×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
28	C₇×#391	C₄	1	1	yes	characteristic
29	C₇×#391	C₄	1	1	yes	characteristic
30	C₇×#389	C₄	1	2	yes	—
31	C₇×#389	C₄	1	2	yes	—
32	C₇×#384	C₄	1	1	yes	characteristic
33	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄³×C₇	C₂²	1	1	yes	characteristic
36	C₇×#336	C₂²	1	2	yes	—
37	C₇×#336	C₂²	1	2	yes	—
38	C₇×#336	C₂²	1	2	yes	—
39	C₇×#336	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	1	yes	characteristic
42	C₇×#336	C₂²	1	2	yes	—
43	#23150	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₇×C₈	C₂³	1	2	yes	—
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₇×C₄⋊Q₈	—	2	4	no	—
53	C₄×C₇×Q₈	—	2	2	no	—
54	C₄×C₇×Q₈	—	2	2	no	—
55	C₄×C₇×Q₈	—	2	2	no	—
56	C₄×C₇×Q₈	—	2	2	no	—
57	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₇×C₄⋊C₈	—	2	4	no	—
75	C₇×C₄⋊C₈	—	2	4	no	—
76	C₇×C₄⋊C₈	—	2	2	no	—
77	C₇×C₄⋊C₈	—	2	2	no	—
78	C₇×C₄⋊C₈	D₄	1	4	yes	—
79	C₇×C₄⋊C₈	Q₈	1	4	yes	complemented
80	C₇×#97	—	2	4	no	—
81	C₇×#97	—	2	4	no	—
82	C₄×C₇×C₈	—	2	4	no	—
83	C₄×C₇×C₈	—	2	2	no	—
84	C₄×C₇×C₈	—	2	2	no	—
85	C₇×#95	C₂×C₄	1	2	yes	—
86	C₇×#95	C₂×C₄	1	2	yes	—
87	C₇×#95	C₂×C₄	1	2	yes	—
88	C₇×#95	C₂×C₄	1	2	yes	—
89	C₂×#446	C₂×C₇	1	1	yes	characteristic
90	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic
91	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic
92	#1984	C₂×C₇	1	1	yes	characteristic
93	#1984	C₂×C₇	1	1	yes	characteristic
94	#1940	C₂×C₇	1	2	yes	—
95	#1917	C₂×C₇	1	2	yes	—
96	#1916	C₂×C₇	1	2	yes	—
97	#1771	C₂×C₇	1	2	yes	—
98	#1767	C₂×C₇	1	1	yes	characteristic
99	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
100	C₂×C₇×Q₈	—	2	2	no	—
101	C₂×C₇×Q₈	—	2	2	no	—
102	C₂×C₇×Q₈	—	2	2	no	—
103	C₂×C₇×Q₈	—	2	2	no	—
104	C₂×C₇×Q₈	—	2	2	no	—
105	C₂×C₇×Q₈	M₁₆	1	4	yes	—
106	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
117	C₂×C₇×C₈	—	2	1	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	1	no	—
122	C₂×C₇×C₈	—	2	1	no	—
123	C₂×C₇×C₈	—	2	1	no	—
124	C₂×C₇×C₈	—	2	1	no	—
125	C₂×C₇×C₈	—	2	2	no	—
126	C₂×C₇×C₈	—	2	1	no	—
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
133	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
134	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
135	C₇×C₄⋊C₄	—	2	4	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	—	2	2	no	—
138	C₇×C₄⋊C₄	—	2	4	no	—
139	C₇×C₄⋊C₄	—	2	4	no	—
140	C₇×C₄⋊C₄	—	2	4	no	—
141	C₇×C₄⋊C₄	—	2	4	no	—
142	C₇×C₄⋊C₄	—	4	2	no	—
143	C₄²×C₇	—	2	2	no	—
144	C₄²×C₇	—	2	2	no	—
145	C₄²×C₇	—	2	2	no	—
146	C₄²×C₇	—	2	2	no	—
147	C₄²×C₇	—	2	2	no	—
148	C₄²×C₇	—	2	2	no	—
149	C₄²×C₇	—	2	2	no	—
150	C₄²×C₇	—	2	1	no	—
151	C₄²×C₇	—	2	1	no	—
152	C₄²×C₇	—	4	1	no	—
153	C₄²×C₇	C₂×D₄	1	2	yes	—
154	C₄²×C₇	C₂×Q₈	1	2	yes	—
155	C₄²×C₇	#41	1	2	yes	—
156	C₄²×C₇	#41	1	2	yes	—
157	C₂×C₄⋊Q₈	C₄×C₇	1	1	yes	characteristic
158	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
159	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
160	#446	—	2	4	no	—
161	C₈×Q₈	—	2	4	no	—
162	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
163	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
164	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
166	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
168	C₂×#97	C₂²×C₇	1	2	yes	—
169	C₂×#97	C₂²×C₇	1	2	yes	—
170	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
171	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
173	#391	C₄×C₇	1	1	yes	characteristic
174	#391	C₄×C₇	1	1	yes	characteristic
175	#389	C₄×C₇	1	2	yes	—
176	#389	C₄×C₇	1	2	yes	—
177	#384	C₄×C₇	1	1	yes	characteristic
178	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
179	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
180	C₄³	C₂²×C₇	1	1	yes	characteristic
181	#336	C₂²×C₇	1	1	yes	characteristic
182	#336	C₂²×C₇	1	2	yes	—
183	#336	C₂²×C₇	1	2	yes	—
184	#336	C₂²×C₇	1	2	yes	—
185	#336	C₂²×C₇	1	1	yes	characteristic
186	#336	C₂²×C₇	1	2	yes	—
187	#336	C₂²×C₇	1	2	yes	—
188	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
189	C₇×Q₈	—	2	8	no	—
190	C₇×Q₈	—	4	4	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	1	no	—
193	C₂×C₄×C₇	—	2	1	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	1	no	—
196	C₂×C₄×C₇	—	2	1	no	—
197	C₂×C₄×C₇	—	2	1	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	2	1	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	—	2	1	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	2	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
216	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
217	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
218	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
219	C₂×C₄×C₇	#131	1	2	yes	—
220	C₂×C₄×C₇	#131	1	2	yes	—
221	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
223	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
226	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
227	C₇×C₈	—	2	4	no	—
228	C₇×C₈	—	2	2	no	—
229	C₇×C₈	—	2	2	no	—
230	C₇×C₈	—	4	1	no	—
231	C₇×C₈	—	4	1	no	—
232	C₇×C₈	—	4	2	no	—
233	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
234	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₇	1	2	yes	—
236	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₇	1	2	yes	—
239	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
241	C₄⋊Q₈	—	2	4	no	—
242	C₄×Q₈	—	2	2	no	—
243	C₄×Q₈	—	2	2	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
254	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
255	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₇	1	2	yes	—
259	C₂×C₄²	C₂³×C₇	1	2	yes	—
260	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
263	C₄⋊C₈	—	2	4	no	—
264	C₄⋊C₈	—	2	4	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	C₇×D₄	1	4	yes	—
268	C₄⋊C₈	C₇×Q₈	1	4	yes	complemented
269	#97	—	2	4	no	—
270	#97	—	2	4	no	—
271	C₄×C₈	—	2	4	no	—
272	C₄×C₈	—	2	2	no	—
273	C₄×C₈	—	2	2	no	—
274	#95	C₂×C₄×C₇	1	2	yes	—
275	#95	C₂×C₄×C₇	1	2	yes	—
276	#95	C₂×C₄×C₇	1	2	yes	—
277	#95	C₂×C₄×C₇	1	2	yes	—
278	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
280	C₂²×C₇	#519	1	1	yes	characteristic
281	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
282	C₂²×C₇	C₂×#131	1	1	yes	characteristic
283	C₂²×C₇	C₂×#131	1	1	yes	characteristic
284	C₂²×C₇	#568	1	1	yes	characteristic
285	C₄×C₇	—	2	4	no	—
286	C₄×C₇	—	2	2	no	—
287	C₄×C₇	—	2	2	no	—
288	C₄×C₇	—	2	2	no	—
289	C₄×C₇	—	2	2	no	—
290	C₄×C₇	—	4	2	no	—
291	C₄×C₇	—	4	2	no	—
292	C₄×C₇	—	4	2	no	—
293	C₄×C₇	—	4	1	no	—
294	C₄×C₇	#435	1	4	yes	—
295	C₄×C₇	#547	1	1	yes	characteristic
296	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
297	C₄×C₇	#556	1	1	yes	characteristic
298	C₄×C₇	#557	1	1	yes	characteristic
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₇×M₁₆	1	4	yes	—
305	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
332	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
333	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	C₂×C₇×D₄	1	2	yes	—
353	C₄²	C₂×C₇×Q₈	1	2	yes	—
354	C₄²	C₇×#41	1	2	yes	—
355	C₄²	C₇×#41	1	2	yes	—
356	C₂×C₇	#2365	1	1	yes	characteristic
357	C₂×C₇	C₂×#435	1	1	yes	characteristic
358	C₂×C₇	#2935	1	1	yes	characteristic
359	C₂×C₇	#2960	1	1	yes	characteristic
360	C₂×C₇	Q₈×M₁₆	1	1	yes	characteristic
361	C₂×C₇	#2984	1	1	yes	characteristic
362	C₂×C₇	#2985	1	1	yes	characteristic
363	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
364	Q₈	—	2	8	no	—
365	Q₈	—	4	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	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	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
389	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
390	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
391	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
392	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
393	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
394	C₂×C₄	C₇×#131	1	2	yes	—
395	C₂×C₄	C₇×#131	1	2	yes	—
396	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
398	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
399	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
400	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
401	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	2	2	no	—
404	C₈	—	2	2	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	2	no	—
408	C₇	#23150	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
410	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
411	C₂²	C₇×#519	1	1	yes	characteristic
412	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
413	C₂²	C₂×C₇×#131	1	1	yes	characteristic
414	C₂²	C₂×C₇×#131	1	1	yes	characteristic
415	C₂²	C₇×#568	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	1	no	—
425	C₄	C₇×#435	1	4	yes	—
426	C₄	C₇×#547	1	1	yes	characteristic
427	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
428	C₄	C₇×#556	1	1	yes	characteristic
429	C₄	C₇×#557	1	1	yes	characteristic
430	C₂	C₇×#2365	1	1	yes	characteristic
431	C₂	C₂×C₇×#435	1	1	yes	characteristic
432	C₂	C₇×#2935	1	1	yes	characteristic
433	C₂	C₇×#2960	1	1	yes	characteristic
434	C₂	C₇×Q₈×M₁₆	1	1	yes	characteristic
435	C₂	C₇×#2984	1	1	yes	characteristic
436	C₂	C₇×#2985	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle, prime radical	C₂³×C₇	C₂³×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
43. #23150	C₇	direct (N × H)
79. C₇×C₄⋊C₈	Q₈	semidirect
268. C₄⋊C₈	C₇×Q₈	semidirect
408. C₇	#23150	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#446	2
C₂×C₇×C₈×Q₈	2
C₄×C₇×C₄⋊Q₈	2
C₇×#1984	2
C₇×#1940	2
C₇×#1917	2
C₇×#1916	2
C₇×#1771	2
C₇×#1767	2
C₄×C₇×C₄⋊C₈	2
#23150	7

Subgroups — C7×#23150 #13200366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23150 #13200366