Subgroups — C₇×#22798 #13200014

Order 1792.

808 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#433	C₂	1	2	yes	maximal, complemented
2	C₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₇×#1955	C₂	1	2	yes	maximal
4	C₇×#1924	C₂	1	2	yes	maximal, complemented
5	C₇×#1923	C₂	1	2	yes	maximal, complemented
6	C₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1798	C₂	1	2	yes	maximal, complemented
8	C₇×#1771	C₂	1	2	yes	maximal, complemented
9	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
11	C₂×C₇×#117	C₂²	1	2	yes	—
12	C₇×#433	—	2	8	no	—
13	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₇×#97	C₂²	1	2	yes	—
24	C₂×C₇×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
26	C₇×#390	C₄	1	1	yes	characteristic
27	C₇×#390	C₄	1	1	yes	characteristic
28	C₇×#389	C₄	1	1	yes	characteristic
29	C₇×#389	C₄	1	1	yes	characteristic
30	C₇×#388	C₄	1	2	yes	—
31	C₇×#388	C₄	1	2	yes	—
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₇×C₂²⋊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	#22798	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₇	C₂³	1	2	yes	—
41	C₂²×C₇×C₈	C₂³	1	2	yes	—
42	C₂²×C₇×C₈	C₂³	1	2	yes	—
43	C₂²×C₇×C₈	C₂³	1	2	yes	—
44	C₂²×C₇×C₈	C₂³	1	2	yes	—
45	C₄×C₇×D₄	—	2	2	no	—
46	C₄×C₇×D₄	—	2	2	no	—
47	C₇×#117	—	2	4	no	—
48	C₇×#117	—	2	4	no	—
49	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₇	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	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₇	C₂³	1	2	yes	—
65	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
67	C₇×C₄⋊C₈	—	2	4	no	—
68	C₇×C₄⋊C₈	—	2	4	no	—
69	C₇×C₄⋊C₈	—	2	2	no	—
70	C₇×C₄⋊C₈	—	4	1	no	—
71	C₇×C₄⋊C₈	—	4	1	no	—
72	C₇×C₄⋊C₈	D₄	1	4	yes	complemented
73	C₇×C₂²⋊C₈	—	2	4	no	—
74	C₇×C₂²⋊C₈	—	2	4	no	—
75	C₇×C₂²⋊C₈	—	4	2	no	—
76	C₇×C₂²⋊C₈	—	4	2	no	—
77	C₇×#97	—	2	4	no	—
78	C₇×#97	—	2	4	no	—
79	C₄×C₇×C₈	—	2	4	no	—
80	C₇×#95	C₂×C₄	1	2	yes	—
81	C₇×#95	C₂×C₄	1	2	yes	—
82	C₇×#95	C₂×C₄	1	2	yes	—
83	C₂×#433	C₂×C₇	1	2	yes	complemented
84	#2293	C₂×C₇	1	1	yes	characteristic
85	#1955	C₂×C₇	1	2	yes	—
86	#1924	C₂×C₇	1	2	yes	complemented
87	#1923	C₂×C₇	1	2	yes	complemented
88	#1842	C₂×C₇	1	1	yes	characteristic, complemented
89	#1798	C₂×C₇	1	2	yes	complemented
90	#1771	C₂×C₇	1	2	yes	complemented
91	#1767	C₂×C₇	1	1	yes	characteristic, complemented
92	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
93	C₂×C₇×D₄	—	2	2	no	—
94	C₂×C₇×D₄	—	4	1	no	—
95	C₂×C₇×D₄	—	4	1	no	—
96	C₂²×C₄×C₇	—	2	2	no	—
97	C₂²×C₄×C₇	—	2	2	no	—
98	C₂²×C₄×C₇	—	2	2	no	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	—	2	2	no	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
112	C₂×C₇×C₈	—	2	2	no	—
113	C₂×C₇×C₈	—	2	2	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	2	no	—
123	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
124	C₇×C₄⋊C₄	—	2	2	no	—
125	C₇×C₄⋊C₄	—	2	4	no	—
126	C₇×C₄⋊C₄	—	2	4	no	—
127	C₇×C₄⋊C₄	—	4	1	no	—
128	C₇×C₄⋊C₄	—	4	1	no	—
129	C₇×C₂²⋊C₄	—	2	4	no	—
130	C₇×C₂²⋊C₄	—	2	4	no	—
131	C₇×C₂²⋊C₄	—	2	4	no	—
132	C₇×C₂²⋊C₄	—	2	4	no	—
133	C₇×C₂²⋊C₄	—	4	2	no	—
134	C₄²×C₇	—	2	2	no	—
135	C₄²×C₇	—	2	2	no	—
136	C₄²×C₇	—	2	2	no	—
137	C₄²×C₇	—	2	1	no	—
138	C₄²×C₇	—	2	1	no	—
139	C₄²×C₇	—	4	1	no	—
140	C₄²×C₇	—	4	1	no	—
141	C₄²×C₇	—	4	1	no	—
142	C₄²×C₇	C₂×D₄	1	2	yes	—
143	C₄²×C₇	#41	1	2	yes	—
144	C₄²×C₇	#41	1	2	yes	—
145	C₄²×C₇	#41	1	2	yes	—
146	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
147	C₂×#117	C₂²×C₇	1	2	yes	—
148	#433	—	2	8	no	—
149	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
150	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
151	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
152	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
153	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
154	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
155	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
156	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
157	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
158	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
159	C₂×#97	C₂²×C₇	1	2	yes	—
160	C₂×#97	C₂²×C₇	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
162	#390	C₄×C₇	1	1	yes	characteristic
163	#390	C₄×C₇	1	1	yes	characteristic
164	#389	C₄×C₇	1	1	yes	characteristic
165	#389	C₄×C₇	1	1	yes	characteristic
166	#388	C₄×C₇	1	2	yes	—
167	#388	C₄×C₇	1	2	yes	—
168	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
169	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
170	C₄³	C₂²×C₇	1	1	yes	characteristic
171	#336	C₂²×C₇	1	2	yes	—
172	#336	C₂²×C₇	1	2	yes	—
173	#336	C₂²×C₇	1	2	yes	—
174	C₂³×C₇	—	2	2	no	—
175	C₂³×C₇	—	2	2	no	—
176	C₂³×C₇	—	2	2	no	—
177	C₂³×C₇	—	2	2	no	—
178	C₂³×C₇	—	2	2	no	—
179	C₂³×C₇	—	2	2	no	—
180	C₂³×C₇	—	2	2	no	—
181	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
182	C₇×D₄	—	4	4	no	—
183	C₂×C₄×C₇	—	2	1	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	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	2	no	—
200	C₂×C₄×C₇	—	2	1	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	—	2	2	no	—
205	C₂×C₄×C₇	—	4	2	no	—
206	C₂×C₄×C₇	—	4	2	no	—
207	C₂×C₄×C₇	—	4	2	no	—
208	C₂×C₄×C₇	—	4	2	no	—
209	C₂×C₄×C₇	#117	1	2	yes	—
210	C₂×C₄×C₇	#117	1	2	yes	—
211	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₇	C₄×D₄	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	C₂×#41	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	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
220	C₇×C₈	—	2	4	no	—
221	C₇×C₈	—	4	2	no	—
222	C₇×C₈	—	4	2	no	—
223	C₇×C₈	—	4	2	no	—
224	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₇	1	2	yes	—
226	C₂²×C₈	C₂³×C₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₇	1	2	yes	—
228	C₂²×C₈	C₂³×C₇	1	2	yes	—
229	C₂²×C₈	C₂³×C₇	1	2	yes	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	#117	—	2	4	no	—
233	#117	—	2	4	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
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	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
241	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
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	C₂×C₄×C₇	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₇	1	2	yes	—
249	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
252	C₄⋊C₈	—	2	4	no	—
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	4	1	no	—
256	C₄⋊C₈	—	4	1	no	—
257	C₄⋊C₈	C₇×D₄	1	4	yes	complemented
258	C₂²⋊C₈	—	2	4	no	—
259	C₂²⋊C₈	—	2	4	no	—
260	C₂²⋊C₈	—	4	2	no	—
261	C₂²⋊C₈	—	4	2	no	—
262	#97	—	2	4	no	—
263	#97	—	2	4	no	—
264	C₄×C₈	—	2	4	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	C₂²×C₇	—	4	2	no	—
269	C₂²×C₇	—	4	2	no	—
270	C₂²×C₇	—	4	2	no	—
271	C₂²×C₇	—	4	2	no	—
272	C₂²×C₇	—	4	2	no	—
273	C₂²×C₇	—	4	2	no	—
274	C₂²×C₇	—	4	2	no	—
275	C₂²×C₇	C₂×#117	1	1	yes	characteristic
276	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
277	C₂²×C₇	#520	1	1	yes	characteristic
278	C₂²×C₇	C₂×#131	1	1	yes	characteristic
279	C₂²×C₇	#568	1	1	yes	characteristic
280	C₂²×C₇	#568	1	1	yes	characteristic
281	C₂²×C₇	#568	1	1	yes	characteristic
282	C₄×C₇	—	2	2	no	—
283	C₄×C₇	—	2	2	no	—
284	C₄×C₇	—	2	2	no	—
285	C₄×C₇	—	2	2	no	—
286	C₄×C₇	—	2	2	no	—
287	C₄×C₇	—	4	2	no	—
288	C₄×C₇	—	4	2	no	—
289	C₄×C₇	—	4	2	no	—
290	C₄×C₇	—	4	1	no	—
291	C₄×C₇	#547	1	1	yes	characteristic
292	C₄×C₇	#550	1	1	yes	characteristic
293	C₄×C₇	#555	1	1	yes	characteristic
294	C₄×C₇	#556	1	1	yes	characteristic
295	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
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	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	C₂×C₇×D₄	1	2	yes	—
346	C₄²	C₇×#41	1	2	yes	—
347	C₄²	C₇×#41	1	2	yes	—
348	C₄²	C₇×#41	1	2	yes	—
349	C₂×C₇	—	8	2	no	—
350	C₂×C₇	#2354	1	1	yes	characteristic
351	C₂×C₇	#2921	1	1	yes	characteristic
352	C₂×C₇	#2925	1	1	yes	characteristic
353	C₂×C₇	#2932	1	1	yes	characteristic
354	C₂×C₇	#2935	1	1	yes	characteristic
355	C₂×C₇	#2992	1	1	yes	characteristic
356	C₂×C₇	#2995	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
365	D₄	—	4	4	no	—
366	C₂×C₄	—	2	1	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	1	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	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₇×#117	1	2	yes	—
393	C₂×C₄	C₇×#117	1	2	yes	—
394	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
395	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
396	C₂×C₄	C₇×#131	1	2	yes	—
397	C₂×C₄	C₂²×C₇×D₄	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	C₂×C₇×#41	1	1	yes	characteristic
401	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
403	C₈	—	2	4	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₇	#22798	1	1	yes	characteristic, direct product factor, Sylow
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	C₂×C₇×#117	1	1	yes	characteristic
416	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
417	C₂²	C₇×#520	1	1	yes	characteristic
418	C₂²	C₂×C₇×#131	1	1	yes	characteristic
419	C₂²	C₇×#568	1	1	yes	characteristic
420	C₂²	C₇×#568	1	1	yes	characteristic
421	C₂²	C₇×#568	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	2	no	—
431	C₄	C₇×#547	1	1	yes	characteristic
432	C₄	C₇×#550	1	1	yes	characteristic
433	C₄	C₇×#555	1	1	yes	characteristic
434	C₄	C₇×#556	1	1	yes	characteristic
435	C₂	—	8	2	no	—
436	C₂	C₇×#2354	1	1	yes	characteristic
437	C₂	C₇×#2921	1	1	yes	characteristic
438	C₂	C₇×#2925	1	1	yes	characteristic
439	C₂	C₇×#2932	1	1	yes	characteristic
440	C₂	C₇×#2935	1	1	yes	characteristic
441	C₂	C₇×#2992	1	1	yes	characteristic
442	C₂	C₇×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂²×C₇×D₄	C₂×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
1. C₂×C₇×#433	C₂	semidirect
4. C₇×#1924	C₂	semidirect
5. C₇×#1923	C₂	semidirect
6. C₇×#1842	C₂	semidirect
7. C₇×#1798	C₂	semidirect
8. C₇×#1771	C₂	semidirect
9. C₇×#1767	C₂	semidirect
38. #22798	C₇	direct (N × H)
72. C₇×C₄⋊C₈	D₄	semidirect
83. C₂×#433	C₂×C₇	semidirect
86. #1924	C₂×C₇	semidirect
87. #1923	C₂×C₇	semidirect
88. #1842	C₂×C₇	semidirect
89. #1798	C₂×C₇	semidirect
90. #1771	C₂×C₇	semidirect
91. #1767	C₂×C₇	semidirect
257. C₄⋊C₈	C₇×D₄	semidirect
407. C₇	#22798	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×#433	2
C₇×#2293	2
C₇×#1955	2
C₇×#1924	2
C₇×#1923	2
C₇×#1842	2
C₇×#1798	2
C₇×#1771	2
C₇×#1767	2
#22798	7

Subgroups — C7×#22798 #13200014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22798 #13200014