Subgroups — C₇×#23248 #13200464

Order 1792.

716 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₇×#1985	C₂	1	2	yes	maximal
3	C₇×#1984	C₂	1	2	yes	maximal
4	C₇×#1940	C₂	1	2	yes	maximal
5	C₇×#1939	C₂	1	1	yes	maximal, characteristic
6	C₇×#1939	C₂	1	1	yes	maximal, characteristic
7	C₇×#1771	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	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×#97	C₂²	1	2	yes	—
21	C₂×C₇×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
25	C₇×#391	C₄	1	2	yes	—
26	C₇×#389	C₄	1	1	yes	characteristic
27	C₇×#389	C₄	1	1	yes	characteristic
28	C₇×#389	C₄	1	2	yes	—
29	C₇×#384	C₄	1	1	yes	characteristic
30	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄³×C₇	C₂²	1	1	yes	characteristic
34	C₇×#336	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	1	yes	characteristic
39	C₇×#336	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	#23248	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
43	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂³	1	2	yes	—
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₇×C₄⋊Q₈	—	2	4	no	—
50	C₄×C₇×Q₈	—	4	2	no	—
51	C₄×C₇×Q₈	—	4	2	no	—
52	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
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×C₄²×C₇	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	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	—	2	2	no	—
72	C₇×C₄⋊C₈	—	4	2	no	—
73	C₇×C₄⋊C₈	—	4	2	no	—
74	C₇×C₄⋊C₈	Q₈	1	4	yes	complemented
75	C₇×C₄⋊C₈	Q₈	1	4	yes	complemented
76	C₇×#97	—	2	4	no	—
77	C₇×#97	—	4	2	no	—
78	C₄×C₇×C₈	—	2	2	no	—
79	C₄×C₇×C₈	—	2	2	no	—
80	C₄×C₇×C₈	—	4	2	no	—
81	C₇×#95	C₂×C₄	1	2	yes	—
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	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic
86	#1985	C₂×C₇	1	2	yes	—
87	#1984	C₂×C₇	1	2	yes	—
88	#1940	C₂×C₇	1	2	yes	—
89	#1939	C₂×C₇	1	1	yes	characteristic
90	#1939	C₂×C₇	1	1	yes	characteristic
91	#1771	C₂×C₇	1	2	yes	—
92	#1770	C₂×C₇	1	1	yes	characteristic
93	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
94	#1767	C₂×C₇	1	1	yes	characteristic
95	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
96	C₂×C₇×Q₈	—	2	4	no	—
97	C₂×C₇×Q₈	—	2	4	no	—
98	C₂×C₇×Q₈	—	4	2	no	—
99	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
107	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
110	C₂×C₇×C₈	—	2	1	no	—
111	C₂×C₇×C₈	—	2	1	no	—
112	C₂×C₇×C₈	—	2	2	no	—
113	C₂×C₇×C₈	—	2	1	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	1	no	—
116	C₂×C₇×C₈	—	2	1	no	—
117	C₂×C₇×C₈	—	2	1	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	2	1	no	—
120	C₂×C₇×C₈	—	2	1	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	1	no	—
123	C₂×C₇×C₈	—	2	1	no	—
124	C₂×C₇×C₈	—	2	2	no	—
125	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
126	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
127	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
128	C₇×C₄⋊C₄	—	2	4	no	—
129	C₇×C₄⋊C₄	—	2	2	no	—
130	C₇×C₄⋊C₄	—	2	2	no	—
131	C₇×C₄⋊C₄	—	2	2	no	—
132	C₇×C₄⋊C₄	—	4	2	no	—
133	C₇×C₄⋊C₄	—	4	2	no	—
134	C₇×C₄⋊C₄	—	4	2	no	—
135	C₇×C₄⋊C₄	—	4	2	no	—
136	C₇×C₄⋊C₄	M₁₆	1	4	yes	—
137	C₄²×C₇	—	2	2	no	—
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	1	no	—
145	C₄²×C₇	—	2	1	no	—
146	C₄²×C₇	—	4	1	no	—
147	C₄²×C₇	C₂×Q₈	1	2	yes	—
148	C₄²×C₇	C₂×Q₈	1	2	yes	—
149	C₄²×C₇	#41	1	2	yes	—
150	C₄²×C₇	#41	1	2	yes	—
151	C₂×C₄⋊Q₈	C₄×C₇	1	1	yes	characteristic
152	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
153	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
154	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
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×#97	C₂²×C₇	1	2	yes	—
160	C₂×#97	C₂²×C₇	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
164	#391	C₄×C₇	1	2	yes	—
165	#389	C₄×C₇	1	1	yes	characteristic
166	#389	C₄×C₇	1	1	yes	characteristic
167	#389	C₄×C₇	1	2	yes	—
168	#384	C₄×C₇	1	1	yes	characteristic
169	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
170	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
172	C₄³	C₂²×C₇	1	1	yes	characteristic
173	#336	C₂²×C₇	1	2	yes	—
174	#336	C₂²×C₇	1	2	yes	—
175	#336	C₂²×C₇	1	2	yes	—
176	#336	C₂²×C₇	1	2	yes	—
177	#336	C₂²×C₇	1	1	yes	characteristic
178	#336	C₂²×C₇	1	2	yes	—
179	#336	C₂²×C₇	1	1	yes	characteristic
180	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
181	C₇×Q₈	—	4	8	no	—
182	C₂×C₄×C₇	—	2	1	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	—	2	1	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	2	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	2	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	1	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
205	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
206	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
207	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
208	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
209	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
210	C₂×C₄×C₇	#131	1	2	yes	—
211	C₂×C₄×C₇	#131	1	2	yes	—
212	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
213	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
218	C₇×C₈	—	2	2	no	—
219	C₇×C₈	—	2	2	no	—
220	C₇×C₈	—	2	4	no	—
221	C₇×C₈	—	4	1	no	—
222	C₇×C₈	—	4	1	no	—
223	C₇×C₈	—	4	2	no	—
224	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
225	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₇	1	2	yes	—
228	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₇	1	2	yes	—
231	C₄⋊Q₈	—	2	4	no	—
232	C₄×Q₈	—	4	2	no	—
233	C₄×Q₈	—	4	2	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
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×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
244	C₂×C₄²	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	C₂³×C₇	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₇	1	2	yes	—
249	C₂×C₄²	C₂³×C₇	1	2	yes	—
250	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	—	4	2	no	—
255	C₄⋊C₈	—	4	2	no	—
256	C₄⋊C₈	C₇×Q₈	1	4	yes	complemented
257	C₄⋊C₈	C₇×Q₈	1	4	yes	complemented
258	#97	—	2	4	no	—
259	#97	—	4	2	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	—	4	2	no	—
263	#95	C₂×C₄×C₇	1	2	yes	—
264	#95	C₂×C₄×C₇	1	2	yes	—
265	#95	C₂×C₄×C₇	1	2	yes	—
266	#95	C₂×C₄×C₇	1	2	yes	—
267	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
268	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
269	C₂²×C₇	#518	1	1	yes	characteristic
270	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
271	C₂²×C₇	C₂×#131	1	1	yes	characteristic
272	C₂²×C₇	C₂×#131	1	1	yes	characteristic
273	C₂²×C₇	#568	1	1	yes	characteristic
274	C₄×C₇	—	2	2	no	—
275	C₄×C₇	—	2	2	no	—
276	C₄×C₇	—	2	2	no	—
277	C₄×C₇	—	2	4	no	—
278	C₄×C₇	—	2	2	no	—
279	C₄×C₇	—	4	2	no	—
280	C₄×C₇	—	4	1	no	—
281	C₄×C₇	—	4	2	no	—
282	C₄×C₇	—	4	2	no	—
283	C₄×C₇	#446	1	4	yes	—
284	C₄×C₇	#554	1	1	yes	characteristic
285	C₄×C₇	#554	1	1	yes	characteristic
286	C₄×C₇	#555	1	1	yes	characteristic
287	C₄×C₇	Q₈²	1	1	yes	characteristic
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	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	C₂×C₇×Q₈	1	2	yes	—
318	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
319	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	C₇×M₁₆	1	4	yes	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
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	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	4	1	no	—
339	C₄²	C₂×C₇×Q₈	1	2	yes	—
340	C₄²	C₂×C₇×Q₈	1	2	yes	—
341	C₄²	C₇×#41	1	2	yes	—
342	C₄²	C₇×#41	1	2	yes	—
343	C₂×C₇	#2369	1	1	yes	characteristic
344	C₂×C₇	C₂×#446	1	1	yes	characteristic
345	C₂×C₇	#2960	1	1	yes	characteristic
346	C₂×C₇	#2962	1	1	yes	characteristic
347	C₂×C₇	Q₈×M₁₆	1	1	yes	characteristic
348	C₂×C₇	#2974	1	1	yes	characteristic
349	C₂×C₇	#2981	1	1	yes	characteristic
350	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
351	Q₈	—	4	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	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	2	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	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
375	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
376	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
377	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
378	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
379	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
380	C₂×C₄	C₇×#131	1	2	yes	—
381	C₂×C₄	C₇×#131	1	2	yes	—
382	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
384	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
385	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
386	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	2	4	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₇	#23248	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
396	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
397	C₂²	C₇×#518	1	1	yes	characteristic
398	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
399	C₂²	C₂×C₇×#131	1	1	yes	characteristic
400	C₂²	C₂×C₇×#131	1	1	yes	characteristic
401	C₂²	C₇×#568	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	4	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	C₇×#446	1	4	yes	—
412	C₄	C₇×#554	1	1	yes	characteristic
413	C₄	C₇×#554	1	1	yes	characteristic
414	C₄	C₇×#555	1	1	yes	characteristic
415	C₄	C₇×Q₈²	1	1	yes	characteristic
416	C₂	C₇×#2369	1	1	yes	characteristic
417	C₂	C₂×C₇×#446	1	1	yes	characteristic
418	C₂	C₇×#2960	1	1	yes	characteristic
419	C₂	C₇×#2962	1	1	yes	characteristic
420	C₂	C₇×Q₈×M₁₆	1	1	yes	characteristic
421	C₂	C₇×#2974	1	1	yes	characteristic
422	C₂	C₇×#2981	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
41. #23248	C₇	direct (N × H)
74. C₇×C₄⋊C₈	Q₈	semidirect
75. C₇×C₄⋊C₈	Q₈	semidirect
256. C₄⋊C₈	C₇×Q₈	semidirect
257. C₄⋊C₈	C₇×Q₈	semidirect
394. C₇	#23248	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₇×C₄⋊Q₈	2
C₇×#1985	2
C₇×#1984	2
C₇×#1940	2
C₇×#1939	2
C₇×#1771	2
C₇×#1770	2
C₇×C₈×C₄⋊C₄	2
C₇×#1767	2
C₄×C₇×C₄⋊C₈	2
#23248	7

Subgroups — C7×#23248 #13200464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23248 #13200464