Subgroups — C₇×#23699 #13200915

Order 1792.

894 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal
4	C₇×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2075	C₂	1	1	yes	maximal, characteristic
6	C₇×#2066	C₂	1	2	yes	maximal, complemented
7	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2035	C₂	1	2	yes	maximal
9	C₇×#2001	C₂	1	1	yes	maximal, characteristic
10	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
15	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
16	C₄×C₇×Q₁₆	—	2	4	no	—
17	C₇×#431	—	2	4	no	—
18	C₂×C₇×#107	C₂²	1	1	yes	characteristic
19	C₂×C₇×#106	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#103	C₂²	1	2	yes	—
23	C₂×C₇×#103	C₂²	1	2	yes	—
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₇×#391	C₂²	1	2	yes	—
30	C₇×#389	C₂²	1	2	yes	—
31	C₇×#387	—	2	2	no	—
32	C₇×#385	—	2	2	no	—
33	C₇×#380	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	—	2	2	no	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₇×C₂²⋊C₄	—	2	2	no	—
37	C₇×#340	C₂²	1	1	yes	characteristic
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	1	yes	characteristic
41	#23699	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×Q₈	C₂³	1	2	yes	—
43	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
46	C₂×C₇×Q₁₆	—	2	4	no	—
47	C₂×C₇×Q₁₆	—	2	2	no	—
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₇×C₂²⋊Q₈	—	2	4	no	—
53	C₇×C₂²⋊Q₈	—	2	4	no	—
54	C₄×C₇×Q₈	—	2	4	no	—
55	C₄×C₇×Q₈	—	2	4	no	—
56	C₂×C₇×C₄⋊C₄	—	2	2	no	—
57	C₂×C₇×C₄⋊C₄	—	2	2	no	—
58	C₂×C₇×C₄⋊C₄	—	2	2	no	—
59	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₇	—	2	2	no	—
65	C₂×C₄²×C₇	—	2	2	no	—
66	C₂×C₄²×C₇	—	2	2	no	—
67	C₂×C₄²×C₇	—	2	2	no	—
68	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×#107	—	2	2	no	—
73	C₇×#106	—	2	4	no	—
74	C₇×C₄⋊C₈	—	2	2	no	—
75	C₇×C₄⋊C₈	—	2	2	no	—
76	C₇×#103	—	2	4	no	—
77	C₇×#103	—	2	4	no	—
78	C₇×#103	—	2	4	no	—
79	C₇×C₂²⋊C₈	—	2	2	no	—
80	C₇×C₂²⋊C₈	—	2	2	no	—
81	C₄×C₇×C₈	—	2	2	no	—
82	C₄×C₇×C₈	D₄	1	4	yes	—
83	C₇×#95	—	2	2	no	—
84	C₇×#95	—	2	2	no	—
85	C₇×#95	—	2	2	no	—
86	C₇×#95	—	2	2	no	—
87	C₇×#95	—	2	2	no	—
88	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
89	C₂×#431	C₂×C₇	1	1	yes	characteristic
90	C₄×C₂²⋊Q₈	C₂×C₇	1	2	yes	—
91	#2086	C₂×C₇	1	1	yes	characteristic, complemented
92	#2075	C₂×C₇	1	1	yes	characteristic
93	#2066	C₂×C₇	1	2	yes	complemented
94	#2056	C₂×C₇	1	1	yes	characteristic, complemented
95	#2035	C₂×C₇	1	2	yes	—
96	#2001	C₂×C₇	1	1	yes	characteristic
97	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
98	C₄×#103	C₂×C₇	1	2	yes	complemented
99	C₂⁴×C₇	C₂×D₄	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	#41	1	4	yes	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	—	2	2	no	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	—	2	2	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	4	no	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
125	C₇×Q₁₆	—	2	8	no	—
126	C₂×C₇×C₈	—	2	2	no	—
127	C₂×C₇×C₈	—	2	2	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	2	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
133	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
134	C₇×C₄⋊C₄	—	2	8	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	—	2	2	no	—
138	C₇×C₄⋊C₄	—	2	2	no	—
139	C₇×C₄⋊C₄	—	2	2	no	—
140	C₇×C₄⋊C₄	—	4	4	no	—
141	C₇×C₄⋊C₄	—	4	4	no	—
142	C₇×C₄⋊C₄	#41	1	4	yes	—
143	C₇×C₂²⋊C₄	—	2	8	no	—
144	C₇×C₂²⋊C₄	—	4	4	no	—
145	C₄²×C₇	—	2	2	no	—
146	C₄²×C₇	—	2	2	no	—
147	C₄²×C₇	—	2	1	no	—
148	C₄²×C₇	—	2	1	no	—
149	C₄²×C₇	—	4	4	no	—
150	C₄²×C₇	—	4	4	no	—
151	C₄²×C₇	C₂×D₄	1	2	yes	—
152	C₄²×C₇	#41	1	2	yes	—
153	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
154	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
155	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
156	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
157	C₄×Q₁₆	—	2	4	no	—
158	#431	—	2	4	no	—
159	C₂×#107	C₂²×C₇	1	1	yes	characteristic
160	C₂×#106	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×#103	C₂²×C₇	1	2	yes	—
164	C₂×#103	C₂²×C₇	1	2	yes	—
165	C₂×#103	C₂²×C₇	1	2	yes	—
166	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
168	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
170	#391	C₂²×C₇	1	2	yes	—
171	#389	C₂²×C₇	1	2	yes	—
172	#387	—	2	2	no	—
173	#385	—	2	2	no	—
174	#380	C₂²×C₇	1	2	yes	—
175	C₄×C₄⋊C₄	—	2	2	no	—
176	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
177	C₄×C₂²⋊C₄	—	2	2	no	—
178	#340	C₂²×C₇	1	1	yes	characteristic
179	#340	C₂²×C₇	1	2	yes	—
180	#340	C₂²×C₇	1	1	yes	characteristic
181	#340	C₂²×C₇	1	2	yes	—
182	C₂³×C₇	—	2	1	no	—
183	C₂³×C₇	—	2	2	no	—
184	C₂³×C₇	—	2	1	no	—
185	C₂³×C₇	—	2	2	no	—
186	C₂³×C₇	#135	1	2	yes	—
187	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
188	C₇×Q₈	—	2	4	no	—
189	C₇×Q₈	—	2	4	no	—
190	C₇×Q₈	—	4	2	no	—
191	C₇×Q₈	—	4	2	no	—
192	C₂×C₄×C₇	—	2	8	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	1	no	—
199	C₂×C₄×C₇	—	2	4	no	—
200	C₂×C₄×C₇	—	2	4	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	4	2	no	—
204	C₂×C₄×C₇	—	4	2	no	—
205	C₂×C₄×C₇	—	4	2	no	—
206	C₂×C₄×C₇	—	4	2	no	—
207	C₂×C₄×C₇	—	4	1	no	—
208	C₂×C₄×C₇	—	4	2	no	—
209	C₂×C₄×C₇	—	4	1	no	—
210	C₂×C₄×C₇	—	4	4	no	—
211	C₂×C₄×C₇	—	4	2	no	—
212	C₂×C₄×C₇	—	4	2	no	—
213	C₂×C₄×C₇	—	4	2	no	—
214	C₂×C₄×C₇	—	4	2	no	—
215	C₂×C₄×C₇	—	4	2	no	—
216	C₂×C₄×C₇	—	4	2	no	—
217	C₂×C₄×C₇	#121	1	2	yes	—
218	C₂×C₄×C₇	#121	1	2	yes	—
219	C₂×C₄×C₇	#135	1	2	yes	—
220	C₂×C₄×C₇	#137	1	4	yes	—
221	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₇	C₂×#41	1	2	yes	—
223	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂×#41	1	2	yes	—
225	C₇×C₈	—	2	2	no	—
226	C₇×C₈	—	2	2	no	—
227	C₇×C₈	—	4	1	no	—
228	C₇×C₈	—	4	1	no	—
229	C₂²×Q₈	C₂³×C₇	1	2	yes	—
230	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
231	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
233	C₂×Q₁₆	—	2	4	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	C₄×Q₈	—	2	4	no	—
242	C₄×Q₈	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
256	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
259	#107	—	2	2	no	—
260	#106	—	2	4	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	2	2	no	—
263	#103	—	2	4	no	—
264	#103	—	2	4	no	—
265	#103	—	2	4	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	C₇×D₄	1	4	yes	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	C₂²×C₇	—	2	4	no	—
276	C₂²×C₇	—	2	2	no	—
277	C₂²×C₇	—	4	2	no	—
278	C₂²×C₇	—	4	1	no	—
279	C₂²×C₇	—	4	1	no	—
280	C₂²×C₇	C₂×#121	1	1	yes	characteristic
281	C₂²×C₇	#525	1	2	yes	—
282	C₂²×C₇	C₂×#135	1	1	yes	characteristic
283	C₂²×C₇	C₂×#135	1	1	yes	characteristic
284	C₂²×C₇	C₂×#137	1	2	yes	—
285	C₄×C₇	—	2	2	no	—
286	C₄×C₇	—	2	2	no	—
287	C₄×C₇	—	4	4	no	—
288	C₄×C₇	—	4	1	no	—
289	C₄×C₇	—	4	4	no	—
290	C₄×C₇	—	4	1	no	—
291	C₄×C₇	—	8	2	no	—
292	C₄×C₇	—	8	2	no	—
293	C₄×C₇	#470	1	4	yes	—
294	C₄×C₇	#525	1	1	yes	characteristic
295	C₄×C₇	#529	1	2	yes	—
296	C₄×C₇	#532	1	1	yes	characteristic
297	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
298	C₂×Q₈	—	2	2	no	—
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	C₇×#41	1	4	yes	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
323	Q₁₆	—	2	8	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
331	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	C₇×#41	1	4	yes	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	4	4	no	—
348	C₄²	—	4	4	no	—
349	C₄²	C₂×C₇×D₄	1	2	yes	—
350	C₄²	C₇×#41	1	2	yes	—
351	C₂×C₇	—	4	2	no	—
352	C₂×C₇	#2392	1	1	yes	characteristic
353	C₂×C₇	#3050	1	1	yes	characteristic
354	C₂×C₇	C₂×#470	1	1	yes	characteristic
355	C₂×C₇	#3107	1	2	yes	—
356	C₂×C₇	#3108	1	2	yes	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	C₇×#135	1	2	yes	—
362	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	C₂×C₄	—	2	8	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	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	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×#121	1	2	yes	—
393	C₂×C₄	C₇×#121	1	2	yes	—
394	C₂×C₄	C₇×#135	1	2	yes	—
395	C₂×C₄	C₇×#137	1	4	yes	—
396	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
397	C₂×C₄	C₂×C₇×#41	1	2	yes	—
398	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
399	C₂×C₄	C₂×C₇×#41	1	2	yes	—
400	C₈	—	2	2	no	—
401	C₈	—	2	2	no	—
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₇	#23699	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	C₂×C₇×#121	1	1	yes	characteristic
411	C₂²	C₇×#525	1	2	yes	—
412	C₂²	C₂×C₇×#135	1	1	yes	characteristic
413	C₂²	C₂×C₇×#135	1	1	yes	characteristic
414	C₂²	C₂×C₇×#137	1	2	yes	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	4	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₇×#470	1	4	yes	—
424	C₄	C₇×#525	1	1	yes	characteristic
425	C₄	C₇×#529	1	2	yes	—
426	C₄	C₇×#532	1	1	yes	characteristic
427	C₂	—	4	2	no	—
428	C₂	C₇×#2392	1	1	yes	characteristic
429	C₂	C₇×#3050	1	1	yes	characteristic
430	C₂	C₂×C₇×#470	1	1	yes	characteristic
431	C₂	C₇×#3107	1	2	yes	—
432	C₂	C₇×#3108	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₇×Q₁₆	C₂	semidirect
4. C₇×#2086	C₂	semidirect
6. C₇×#2066	C₂	semidirect
7. C₇×#2056	C₂	semidirect
10. C₄×C₇×#106	C₂	semidirect
11. C₄×C₇×#103	C₂	semidirect
41. #23699	C₇	direct (N × H)
88. C₂×C₄×Q₁₆	C₂×C₇	semidirect
91. #2086	C₂×C₇	semidirect
93. #2066	C₂×C₇	semidirect
94. #2056	C₂×C₇	semidirect
97. C₄×#106	C₂×C₇	semidirect
98. C₄×#103	C₂×C₇	semidirect
404. C₇	#23699	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×C₄×C₇×Q₁₆	2
C₂×C₇×#431	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2086	2
C₇×#2075	2
C₇×#2066	2
C₇×#2056	2
C₇×#2035	2
C₇×#2001	2
C₄×C₇×#106	2
C₄×C₇×#103	2
#23699	7

Subgroups — C7×#23699 #13200915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23699 #13200915