Subgroups — C₇×#23189 #13200405

Order 1792.

1026 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2367	C₂	1	2	yes	maximal, complemented
5	C₇×#1983	C₂	1	2	yes	maximal, complemented
6	C₇×#1972	C₂	1	1	yes	maximal, characteristic
7	C₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1880	C₂	1	2	yes	maximal, complemented
9	C₇×#1877	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#124	C₂²	1	2	yes	—
16	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
17	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
18	C₇×#495	C₄	1	8	yes	complemented
19	C₇×#442	—	2	4	no	—
20	C₇×#441	—	2	4	no	—
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×#103	C₂²	1	2	yes	—
26	C₂×C₇×#102	C₂²	1	2	yes	—
27	C₂×C₇×#102	C₂²	1	2	yes	—
28	C₂×C₇×#97	C₂²	1	1	yes	characteristic
29	C₂×C₇×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₇×#391	C₂²	1	2	yes	—
32	C₇×#390	C₂²	1	2	yes	—
33	C₇×#388	—	2	2	no	—
34	C₇×#388	—	2	2	no	—
35	C₇×#385	—	2	2	no	—
36	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₂²⋊C₄	—	2	2	no	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	1	yes	characteristic
42	#23189	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	2	yes	—
44	C₂²×C₇×D₄	C₂³	1	2	yes	—
45	C₂³×C₄×C₇	—	2	2	no	—
46	C₂×C₇×Q₁₆	—	2	2	no	—
47	C₂×C₇×Q₁₆	—	2	2	no	—
48	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₂×C₇×SD₁₆	—	4	2	no	—
50	C₂×C₇×SD₁₆	—	4	2	no	—
51	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	complemented
52	C₂×C₇×D₈	—	2	2	no	—
53	C₂×C₇×D₈	—	2	2	no	—
54	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₇×#124	—	2	4	no	—
60	C₇×#124	C₂×C₄	1	8	yes	complemented
61	C₄×C₇×Q₈	—	2	4	no	—
62	C₄×C₇×Q₈	—	4	2	no	—
63	C₄×C₇×D₄	—	2	4	no	—
64	C₄×C₇×D₄	—	4	2	no	—
65	C₂×C₇×C₄⋊C₄	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₄²×C₇	—	2	2	no	—
75	C₂×C₄²×C₇	—	2	2	no	—
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₇×#106	—	2	2	no	—
80	C₇×#106	D₄	1	4	yes	—
81	C₇×C₄⋊C₈	—	2	2	no	—
82	C₇×#103	—	2	4	no	—
83	C₇×#103	—	4	2	no	—
84	C₇×#102	—	2	4	no	—
85	C₇×#102	—	4	2	no	—
86	C₇×#97	—	2	2	no	—
87	C₇×#97	—	2	2	no	—
88	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
89	C₇×#95	—	2	2	no	—
90	C₇×#95	—	2	2	no	—
91	C₇×#95	—	2	2	no	—
92	C₇×#95	D₄	1	2	yes	—
93	C₂×#495	C₂×C₇	1	1	yes	characteristic
94	C₂×#442	C₂×C₇	1	1	yes	characteristic
95	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
96	#2367	C₂×C₇	1	2	yes	complemented
97	#1983	C₂×C₇	1	2	yes	complemented
98	#1972	C₂×C₇	1	1	yes	characteristic
99	#1971	C₂×C₇	1	1	yes	characteristic, complemented
100	#1880	C₂×C₇	1	2	yes	complemented
101	#1877	C₂×C₇	1	2	yes	complemented
102	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
103	#1770	C₂×C₇	1	1	yes	characteristic, complemented
104	C₂⁴×C₇	—	2	2	no	—
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂×C₇×Q₈	—	2	2	no	—
107	C₂×C₇×Q₈	—	2	2	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×Q₈	—	2	2	no	—
110	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	2	2	no	—
115	C₂×C₇×D₄	—	2	2	no	—
116	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	4	4	no	—
121	C₂²×C₄×C₇	—	4	4	no	—
122	C₂²×C₄×C₇	—	8	2	no	—
123	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
128	C₇×Q₁₆	—	2	8	no	—
129	C₇×SD₁₆	—	4	8	no	—
130	C₇×D₈	—	2	8	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	1	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₇×C₈	#41	1	2	yes	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	4	2	no	—
147	C₇×C₄⋊C₄	—	4	4	no	—
148	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
149	C₇×C₂²⋊C₄	—	2	8	no	—
150	C₇×C₂²⋊C₄	—	2	8	no	—
151	C₇×C₂²⋊C₄	—	4	4	no	—
152	C₇×C₂²⋊C₄	—	4	4	no	—
153	C₇×C₂²⋊C₄	—	8	2	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	—	2	1	no	—
156	C₄²×C₇	—	2	1	no	—
157	C₄²×C₇	—	2	1	no	—
158	C₄²×C₇	—	4	4	no	—
159	C₄²×C₇	—	8	2	no	—
160	C₄²×C₇	C₂²×C₄	1	2	yes	—
161	C₄²×C₇	#41	1	2	yes	—
162	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
163	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
164	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×#124	C₂²×C₇	1	2	yes	—
166	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
167	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
168	#495	C₄×C₇	1	8	yes	complemented
169	#442	—	2	4	no	—
170	#441	—	2	4	no	—
171	C₂×#106	C₂²×C₇	1	1	yes	characteristic
172	C₂×#106	C₂²×C₇	1	1	yes	characteristic
173	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
174	C₂×#103	C₂²×C₇	1	2	yes	—
175	C₂×#103	C₂²×C₇	1	2	yes	—
176	C₂×#102	C₂²×C₇	1	2	yes	—
177	C₂×#102	C₂²×C₇	1	2	yes	—
178	C₂×#97	C₂²×C₇	1	1	yes	characteristic
179	C₂×#97	C₂²×C₇	1	1	yes	characteristic
180	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
181	#391	C₂²×C₇	1	2	yes	—
182	#390	C₂²×C₇	1	2	yes	—
183	#388	—	2	2	no	—
184	#388	—	2	2	no	—
185	#385	—	2	2	no	—
186	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
187	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
188	C₄×C₂²⋊C₄	—	2	2	no	—
189	#340	C₂²×C₇	1	2	yes	—
190	#336	C₂²×C₇	1	1	yes	characteristic
191	#336	C₂²×C₇	1	1	yes	characteristic
192	C₂³×C₇	—	2	4	no	—
193	C₂³×C₇	—	4	2	no	—
194	C₂³×C₇	—	4	2	no	—
195	C₂³×C₇	—	4	2	no	—
196	C₂³×C₇	—	4	2	no	—
197	C₂³×C₇	—	4	2	no	—
198	C₂³×C₇	—	4	2	no	—
199	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
200	C₇×Q₈	—	2	4	no	—
201	C₇×Q₈	—	2	4	no	—
202	C₇×Q₈	—	4	2	no	—
203	C₇×Q₈	—	4	2	no	—
204	C₇×D₄	—	2	4	no	—
205	C₇×D₄	—	2	4	no	—
206	C₇×D₄	—	4	2	no	—
207	C₇×D₄	—	4	2	no	—
208	C₂×C₄×C₇	—	2	2	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	4	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	4	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	2	2	no	—
216	C₂×C₄×C₇	—	2	2	no	—
217	C₂×C₄×C₇	—	2	2	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	—	4	2	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	—	4	2	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	8	8	no	—
226	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
234	C₇×C₈	—	2	2	no	—
235	C₇×C₈	—	4	1	no	—
236	C₇×C₈	—	4	1	no	—
237	C₇×C₈	C₄×D₄	1	4	yes	—
238	C₂²×Q₈	C₂³×C₇	1	2	yes	—
239	C₂²×D₄	C₂³×C₇	1	2	yes	—
240	C₂³×C₄	—	2	2	no	—
241	C₂×Q₁₆	—	2	2	no	—
242	C₂×Q₁₆	—	2	2	no	—
243	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
244	C₂×SD₁₆	—	4	2	no	—
245	C₂×SD₁₆	—	4	2	no	—
246	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
247	C₂×D₈	—	2	2	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
250	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
254	#124	—	2	4	no	—
255	#124	C₂×C₄×C₇	1	8	yes	complemented
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	—	4	2	no	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	4	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
274	#106	—	2	2	no	—
275	#106	C₇×D₄	1	4	yes	—
276	C₄⋊C₈	—	2	2	no	—
277	#103	—	2	4	no	—
278	#103	—	4	2	no	—
279	#102	—	2	4	no	—
280	#102	—	4	2	no	—
281	#97	—	2	2	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	C₇×D₄	1	2	yes	—
288	C₂²×C₇	—	4	4	no	—
289	C₂²×C₇	—	4	4	no	—
290	C₂²×C₇	—	4	4	no	—
291	C₂²×C₇	—	8	2	no	—
292	C₂²×C₇	—	8	2	no	—
293	C₂²×C₇	—	8	2	no	—
294	C₂²×C₇	—	8	2	no	—
295	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
296	C₂²×C₇	D₄²	1	1	yes	characteristic
297	C₂²×C₇	#550	1	1	yes	characteristic
298	C₂²×C₇	#575	1	2	yes	—
299	C₂²×C₇	#577	1	2	yes	—
300	C₄×C₇	—	2	2	no	—
301	C₄×C₇	—	2	2	no	—
302	C₄×C₇	—	4	4	no	—
303	C₄×C₇	—	4	2	no	—
304	C₄×C₇	—	4	2	no	—
305	C₄×C₇	—	4	4	no	—
306	C₄×C₇	—	8	2	no	—
307	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
308	C₄×C₇	#518	1	1	yes	characteristic
309	C₄×C₇	#550	1	1	yes	characteristic
310	C₄×C₇	#559	1	1	yes	characteristic
311	C₂⁴	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
331	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
332	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
335	Q₁₆	—	2	8	no	—
336	SD₁₆	—	4	8	no	—
337	D₈	—	2	8	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
347	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
348	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
349	C₂×C₈	C₇×#41	1	2	yes	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	2	8	no	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	4	4	no	—
366	C₄²	—	8	2	no	—
367	C₄²	C₂²×C₄×C₇	1	2	yes	—
368	C₄²	C₇×#41	1	2	yes	—
369	C₂×C₇	—	8	4	no	—
370	C₂×C₇	#2366	1	1	yes	characteristic
371	C₂×C₇	#2943	1	1	yes	characteristic
372	C₂×C₇	#2952	1	1	yes	characteristic
373	C₂×C₇	#3275	1	2	yes	—
374	C₂×C₇	#3401	1	2	yes	—
375	C₂³	—	2	4	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	2	4	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	D₄	—	2	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
410	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
411	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
414	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
415	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	C₄×C₇×D₄	1	4	yes	—
421	C₇	#23189	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
430	C₂²	C₇×D₄²	1	1	yes	characteristic
431	C₂²	C₇×#550	1	1	yes	characteristic
432	C₂²	C₇×#575	1	2	yes	—
433	C₂²	C₇×#577	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	8	2	no	—
441	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
442	C₄	C₇×#518	1	1	yes	characteristic
443	C₄	C₇×#550	1	1	yes	characteristic
444	C₄	C₇×#559	1	1	yes	characteristic
445	C₂	—	8	4	no	—
446	C₂	C₇×#2366	1	1	yes	characteristic
447	C₂	C₇×#2943	1	1	yes	characteristic
448	C₂	C₇×#2952	1	1	yes	characteristic
449	C₂	C₇×#3275	1	2	yes	—
450	C₂	C₇×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₇×#441	C₂	semidirect
4. C₇×#2367	C₂	semidirect
5. C₇×#1983	C₂	semidirect
7. C₇×#1971	C₂	semidirect
8. C₇×#1880	C₂	semidirect
9. C₇×#1877	C₂	semidirect
10. C₄×C₇×#106	C₂	semidirect
11. C₇×#1770	C₂	semidirect
18. C₇×#495	C₄	semidirect
42. #23189	C₇	direct (N × H)
48. C₂×C₇×Q₁₆	C₂×C₄	semidirect
51. C₂×C₇×SD₁₆	C₂×C₄	semidirect
60. C₇×#124	C₂×C₄	semidirect
88. C₄×C₇×C₈	C₂×C₄	semidirect
95. C₂×#441	C₂×C₇	semidirect
96. #2367	C₂×C₇	semidirect
97. #1983	C₂×C₇	semidirect
99. #1971	C₂×C₇	semidirect
100. #1880	C₂×C₇	semidirect
101. #1877	C₂×C₇	semidirect
102. C₄×#106	C₂×C₇	semidirect
103. #1770	C₂×C₇	semidirect
168. #495	C₄×C₇	semidirect
243. C₂×Q₁₆	C₂×C₄×C₇	semidirect
246. C₂×SD₁₆	C₂×C₄×C₇	semidirect
255. #124	C₂×C₄×C₇	semidirect
283. C₄×C₈	C₂×C₄×C₇	semidirect
421. C₇	#23189	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×#495	2
C₂×C₇×#442	2
C₂×C₇×#441	2
C₇×#2367	2
C₇×#1983	2
C₇×#1972	2
C₇×#1971	2
C₇×#1880	2
C₇×#1877	2
C₄×C₇×#106	2
C₇×#1770	2
#23189	7

Subgroups — C7×#23189 #13200405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23189 #13200405