Subgroups — C₇×#23151 #13200367

Order 1792.

772 conjugacy classes of subgroups.

The subgroup lattice has 426 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	2	yes	maximal
2	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#1985	C₂	1	2	yes	maximal
4	C₇×#1939	C₂	1	1	yes	maximal, characteristic
5	C₇×#1939	C₂	1	1	yes	maximal, characteristic
6	C₇×#1917	C₂	1	2	yes	maximal
7	C₇×#1916	C₂	1	2	yes	maximal
8	C₇×#1770	C₂	1	1	yes	maximal, characteristic
9	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
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	2	yes	—
14	C₇×#446	—	2	8	no	—
15	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#97	C₂²	1	2	yes	—
22	C₂×C₇×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
26	C₇×#391	C₄	1	2	yes	—
27	C₇×#389	C₄	1	1	yes	characteristic
28	C₇×#389	C₄	1	2	yes	—
29	C₇×#389	C₄	1	1	yes	characteristic
30	C₇×#384	C₄	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄³×C₇	C₂²	1	1	yes	characteristic
35	C₇×#336	C₂²	1	2	yes	—
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	1	yes	characteristic
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	2	yes	—
42	#23151	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
44	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂³	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	C₇×C₄⋊Q₈	—	2	4	no	—
51	C₄×C₇×Q₈	—	2	4	no	—
52	C₄×C₇×Q₈	—	2	4	no	—
53	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
71	C₇×C₄⋊C₈	—	2	4	no	—
72	C₇×C₄⋊C₈	—	2	4	no	—
73	C₇×C₄⋊C₈	—	2	2	no	—
74	C₇×C₄⋊C₈	—	2	2	no	—
75	C₇×C₄⋊C₈	D₄	1	4	yes	—
76	C₇×C₄⋊C₈	Q₈	1	4	yes	complemented
77	C₇×#97	—	2	4	no	—
78	C₇×#97	—	2	4	no	—
79	C₄×C₇×C₈	—	2	4	no	—
80	C₄×C₇×C₈	—	2	2	no	—
81	C₄×C₇×C₈	—	2	2	no	—
82	C₇×#95	C₂×C₄	1	2	yes	—
83	C₇×#95	C₂×C₄	1	2	yes	—
84	C₇×#95	C₂×C₄	1	2	yes	—
85	C₇×#95	C₂×C₄	1	2	yes	—
86	C₂×#446	C₂×C₇	1	2	yes	—
87	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic
88	#1985	C₂×C₇	1	2	yes	—
89	#1939	C₂×C₇	1	1	yes	characteristic
90	#1939	C₂×C₇	1	1	yes	characteristic
91	#1917	C₂×C₇	1	2	yes	—
92	#1916	C₂×C₇	1	2	yes	—
93	#1770	C₂×C₇	1	1	yes	characteristic
94	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
95	#1767	C₂×C₇	1	1	yes	characteristic
96	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
97	C₂×C₇×Q₈	—	2	4	no	—
98	C₂×C₇×Q₈	—	2	4	no	—
99	C₂×C₇×Q₈	—	4	2	no	—
100	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
109	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
111	C₂×C₇×C₈	—	2	2	no	—
112	C₂×C₇×C₈	—	2	1	no	—
113	C₂×C₇×C₈	—	2	1	no	—
114	C₂×C₇×C₈	—	2	1	no	—
115	C₂×C₇×C₈	—	2	1	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	1	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	2	no	—
124	C₂×C₇×C₈	—	2	1	no	—
125	C₂×C₇×C₈	—	2	1	no	—
126	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
127	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
128	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
129	C₇×C₄⋊C₄	—	2	4	no	—
130	C₇×C₄⋊C₄	—	2	4	no	—
131	C₇×C₄⋊C₄	—	2	4	no	—
132	C₇×C₄⋊C₄	—	2	4	no	—
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	4	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	M₁₆	1	4	yes	—
138	C₄²×C₇	—	2	2	no	—
139	C₄²×C₇	—	2	2	no	—
140	C₄²×C₇	—	2	2	no	—
141	C₄²×C₇	—	2	2	no	—
142	C₄²×C₇	—	2	2	no	—
143	C₄²×C₇	—	2	2	no	—
144	C₄²×C₇	—	2	2	no	—
145	C₄²×C₇	—	2	1	no	—
146	C₄²×C₇	—	2	1	no	—
147	C₄²×C₇	—	4	1	no	—
148	C₄²×C₇	C₂×D₄	1	2	yes	—
149	C₄²×C₇	C₂×Q₈	1	2	yes	—
150	C₄²×C₇	#41	1	2	yes	—
151	C₄²×C₇	#41	1	2	yes	—
152	C₂×C₄⋊Q₈	C₄×C₇	1	1	yes	characteristic
153	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
154	#446	—	2	8	no	—
155	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
156	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
157	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
159	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
160	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
161	C₂×#97	C₂²×C₇	1	2	yes	—
162	C₂×#97	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	#391	C₄×C₇	1	2	yes	—
167	#389	C₄×C₇	1	1	yes	characteristic
168	#389	C₄×C₇	1	2	yes	—
169	#389	C₄×C₇	1	1	yes	characteristic
170	#384	C₄×C₇	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
172	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
173	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
174	C₄³	C₂²×C₇	1	1	yes	characteristic
175	#336	C₂²×C₇	1	1	yes	characteristic
176	#336	C₂²×C₇	1	2	yes	—
177	#336	C₂²×C₇	1	2	yes	—
178	#336	C₂²×C₇	1	2	yes	—
179	#336	C₂²×C₇	1	1	yes	characteristic
180	#336	C₂²×C₇	1	2	yes	—
181	#336	C₂²×C₇	1	2	yes	—
182	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
183	C₇×Q₈	—	4	8	no	—
184	C₂×C₄×C₇	—	2	2	no	—
185	C₂×C₄×C₇	—	2	1	no	—
186	C₂×C₄×C₇	—	2	1	no	—
187	C₂×C₄×C₇	—	2	1	no	—
188	C₂×C₄×C₇	—	2	1	no	—
189	C₂×C₄×C₇	—	2	1	no	—
190	C₂×C₄×C₇	—	2	1	no	—
191	C₂×C₄×C₇	—	2	1	no	—
192	C₂×C₄×C₇	—	2	1	no	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	2	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	2	2	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	2	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	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
209	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
210	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
211	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
212	C₂×C₄×C₇	#131	1	2	yes	—
213	C₂×C₄×C₇	#131	1	2	yes	—
214	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
219	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
220	C₇×C₈	—	2	2	no	—
221	C₇×C₈	—	2	2	no	—
222	C₇×C₈	—	2	4	no	—
223	C₇×C₈	—	4	2	no	—
224	C₇×C₈	—	4	1	no	—
225	C₇×C₈	—	4	1	no	—
226	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₇	1	2	yes	—
230	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₇	1	2	yes	—
233	C₄⋊Q₈	—	2	4	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
246	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
247	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
248	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₇	1	2	yes	—
250	C₂×C₄²	C₂³×C₇	1	2	yes	—
251	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
254	C₄⋊C₈	—	2	4	no	—
255	C₄⋊C₈	—	2	4	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	C₇×D₄	1	4	yes	—
259	C₄⋊C₈	C₇×Q₈	1	4	yes	complemented
260	#97	—	2	4	no	—
261	#97	—	2	4	no	—
262	C₄×C₈	—	2	4	no	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	—	2	2	no	—
265	#95	C₂×C₄×C₇	1	2	yes	—
266	#95	C₂×C₄×C₇	1	2	yes	—
267	#95	C₂×C₄×C₇	1	2	yes	—
268	#95	C₂×C₄×C₇	1	2	yes	—
269	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
271	C₂²×C₇	#519	1	1	yes	characteristic
272	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
273	C₂²×C₇	C₂×#131	1	1	yes	characteristic
274	C₂²×C₇	C₂×#131	1	1	yes	characteristic
275	C₂²×C₇	#568	1	1	yes	characteristic
276	C₄×C₇	—	2	2	no	—
277	C₄×C₇	—	2	2	no	—
278	C₄×C₇	—	2	4	no	—
279	C₄×C₇	—	2	2	no	—
280	C₄×C₇	—	2	2	no	—
281	C₄×C₇	—	4	2	no	—
282	C₄×C₇	—	4	2	no	—
283	C₄×C₇	—	4	2	no	—
284	C₄×C₇	—	4	1	no	—
285	C₄×C₇	#446	1	4	yes	complemented
286	C₄×C₇	#547	1	1	yes	characteristic
287	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
288	C₄×C₇	#556	1	1	yes	characteristic
289	C₄×C₇	#557	1	1	yes	characteristic
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
296	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
320	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
321	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	C₇×M₁₆	1	4	yes	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	4	1	no	—
341	C₄²	C₂×C₇×D₄	1	2	yes	—
342	C₄²	C₂×C₇×Q₈	1	2	yes	—
343	C₄²	C₇×#41	1	2	yes	—
344	C₄²	C₇×#41	1	2	yes	—
345	C₂×C₇	#2365	1	1	yes	characteristic
346	C₂×C₇	#2931	1	1	yes	characteristic
347	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
348	C₂×C₇	C₂×#446	1	1	yes	characteristic
349	C₂×C₇	#2962	1	1	yes	characteristic
350	C₂×C₇	#2984	1	1	yes	characteristic
351	C₂×C₇	#2985	1	1	yes	characteristic
352	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
353	Q₈	—	4	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
377	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
378	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
379	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
380	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
381	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
382	C₂×C₄	C₇×#131	1	2	yes	—
383	C₂×C₄	C₇×#131	1	2	yes	—
384	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
386	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
387	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
388	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
389	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₇	#23151	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
398	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
399	C₂²	C₇×#519	1	1	yes	characteristic
400	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
401	C₂²	C₂×C₇×#131	1	1	yes	characteristic
402	C₂²	C₂×C₇×#131	1	1	yes	characteristic
403	C₂²	C₇×#568	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	1	no	—
413	C₄	C₇×#446	1	4	yes	complemented
414	C₄	C₇×#547	1	1	yes	characteristic
415	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
416	C₄	C₇×#556	1	1	yes	characteristic
417	C₄	C₇×#557	1	1	yes	characteristic
418	C₂	C₇×#2365	1	1	yes	characteristic
419	C₂	C₇×#2931	1	1	yes	characteristic
420	C₂	C₇×D₄×M₁₆	1	1	yes	characteristic
421	C₂	C₂×C₇×#446	1	1	yes	characteristic
422	C₂	C₇×#2962	1	1	yes	characteristic
423	C₂	C₇×#2984	1	1	yes	characteristic
424	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
42. #23151	C₇	direct (N × H)
76. C₇×C₄⋊C₈	Q₈	semidirect
259. C₄⋊C₈	C₇×Q₈	semidirect
285. C₄×C₇	#446	semidirect
396. C₇	#23151	direct (N × H)
413. C₄	C₇×#446	semidirect

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
C₄×C₇×C₄⋊Q₈	2
C₇×#1985	2
C₇×#1939	2
C₇×#1917	2
C₇×#1916	2
C₇×#1770	2
C₇×C₈×C₄⋊C₄	2
C₇×#1767	2
C₄×C₇×C₄⋊C₈	2
#23151	7

Subgroups — C7×#23151 #13200367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23151 #13200367