Subgroups — C₇×#23191 #13200407

Order 1792.

1026 conjugacy classes of subgroups.

The subgroup lattice has 440 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×#440	C₂	1	2	yes	maximal, complemented
3	C₇×#2367	C₂	1	2	yes	maximal, complemented
4	C₇×#1983	C₂	1	2	yes	maximal, complemented
5	C₇×#1973	C₂	1	2	yes	maximal, complemented
6	C₇×#1879	C₂	1	2	yes	maximal
7	C₇×#1878	C₂	1	2	yes	maximal, complemented
8	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
12	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×#124	C₂²	1	2	yes	—
14	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
16	C₇×#495	C₄	1	8	yes	complemented
17	C₇×#440	—	2	8	no	—
18	C₂×C₇×#107	C₂²	1	1	yes	characteristic
19	C₂×C₇×#107	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#103	C₂²	1	2	yes	—
22	C₂×C₇×#103	C₂²	1	2	yes	—
23	C₂×C₇×#102	C₂²	1	2	yes	—
24	C₂×C₇×#102	C₂²	1	2	yes	—
25	C₂×C₇×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₇×#391	C₂²	1	2	yes	—
28	C₇×#390	C₂²	1	2	yes	—
29	C₇×#388	—	2	2	no	—
30	C₇×#388	—	2	2	no	—
31	C₇×#385	—	2	2	no	—
32	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₇×C₂²⋊C₄	—	2	2	no	—
35	C₇×#340	C₂²	1	2	yes	—
36	C₇×#336	C₂²	1	2	yes	—
37	#23191	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₇×Q₈	C₂³	1	2	yes	—
39	C₂²×C₇×D₄	C₂³	1	2	yes	—
40	C₂³×C₄×C₇	—	2	2	no	—
41	C₂×C₇×Q₁₆	—	4	1	no	—
42	C₂×C₇×Q₁₆	—	4	1	no	—
43	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
44	C₂×C₇×SD₁₆	—	2	4	no	—
45	C₂×C₇×SD₁₆	—	2	4	no	—
46	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	complemented
47	C₂×C₇×D₈	—	4	1	no	—
48	C₂×C₇×D₈	—	4	1	no	—
49	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
50	C₂²×C₇×C₈	C₂³	1	2	yes	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₇×#124	—	2	4	no	—
54	C₇×#124	C₂×C₄	1	8	yes	complemented
55	C₄×C₇×Q₈	—	2	4	no	—
56	C₄×C₇×Q₈	—	4	2	no	—
57	C₄×C₇×D₄	—	2	4	no	—
58	C₄×C₇×D₄	—	4	2	no	—
59	C₂×C₇×C₄⋊C₄	—	2	2	no	—
60	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₇	—	2	2	no	—
70	C₂×C₄²×C₇	—	2	2	no	—
71	C₂×C₄²×C₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₇×#107	—	2	2	no	—
74	C₇×#107	D₄	1	4	yes	—
75	C₇×C₄⋊C₈	—	2	2	no	—
76	C₇×#103	—	2	4	no	—
77	C₇×#103	—	4	2	no	—
78	C₇×#102	—	2	4	no	—
79	C₇×#102	—	4	2	no	—
80	C₇×#97	—	2	4	no	—
81	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
82	C₇×#95	—	2	2	no	—
83	C₇×#95	—	2	2	no	—
84	C₇×#95	—	2	2	no	—
85	C₇×#95	D₄	1	2	yes	—
86	C₂×#495	C₂×C₇	1	1	yes	characteristic
87	C₂×#440	C₂×C₇	1	2	yes	complemented
88	#2367	C₂×C₇	1	2	yes	complemented
89	#1983	C₂×C₇	1	2	yes	complemented
90	#1973	C₂×C₇	1	2	yes	complemented
91	#1879	C₂×C₇	1	2	yes	—
92	#1878	C₂×C₇	1	2	yes	complemented
93	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
94	#1770	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂⁴×C₇	—	2	2	no	—
96	C₂×C₇×Q₈	—	2	2	no	—
97	C₂×C₇×Q₈	—	2	2	no	—
98	C₂×C₇×Q₈	—	2	2	no	—
99	C₂×C₇×Q₈	—	2	2	no	—
100	C₂×C₇×Q₈	—	2	2	no	—
101	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
102	C₂×C₇×D₄	—	2	2	no	—
103	C₂×C₇×D₄	—	2	2	no	—
104	C₂×C₇×D₄	—	2	2	no	—
105	C₂×C₇×D₄	—	2	2	no	—
106	C₂×C₇×D₄	—	2	2	no	—
107	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
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	—	4	4	no	—
112	C₂²×C₄×C₇	—	4	4	no	—
113	C₂²×C₄×C₇	—	8	2	no	—
114	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
119	C₇×Q₁₆	—	4	4	no	—
120	C₇×SD₁₆	—	2	16	no	—
121	C₇×D₈	—	4	4	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	—	2	2	no	—
126	C₂×C₇×C₈	—	2	2	no	—
127	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
128	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
130	C₂×C₇×C₈	#41	1	2	yes	—
131	C₇×C₄⋊C₄	—	2	2	no	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	4	1	no	—
135	C₇×C₄⋊C₄	—	4	1	no	—
136	C₇×C₄⋊C₄	—	4	4	no	—
137	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
138	C₇×C₂²⋊C₄	—	2	8	no	—
139	C₇×C₂²⋊C₄	—	2	8	no	—
140	C₇×C₂²⋊C₄	—	4	4	no	—
141	C₇×C₂²⋊C₄	—	4	4	no	—
142	C₇×C₂²⋊C₄	—	8	2	no	—
143	C₄²×C₇	—	2	2	no	—
144	C₄²×C₇	—	2	2	no	—
145	C₄²×C₇	—	4	4	no	—
146	C₄²×C₇	—	8	2	no	—
147	C₄²×C₇	C₂²×C₄	1	2	yes	—
148	C₄²×C₇	#41	1	2	yes	—
149	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
150	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
151	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
152	C₂×#124	C₂²×C₇	1	2	yes	—
153	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
154	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
155	#495	C₄×C₇	1	8	yes	complemented
156	#440	—	2	8	no	—
157	C₂×#107	C₂²×C₇	1	1	yes	characteristic
158	C₂×#107	C₂²×C₇	1	1	yes	characteristic
159	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
160	C₂×#103	C₂²×C₇	1	2	yes	—
161	C₂×#103	C₂²×C₇	1	2	yes	—
162	C₂×#102	C₂²×C₇	1	2	yes	—
163	C₂×#102	C₂²×C₇	1	2	yes	—
164	C₂×#97	C₂²×C₇	1	2	yes	—
165	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
166	#391	C₂²×C₇	1	2	yes	—
167	#390	C₂²×C₇	1	2	yes	—
168	#388	—	2	2	no	—
169	#388	—	2	2	no	—
170	#385	—	2	2	no	—
171	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
172	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
173	C₄×C₂²⋊C₄	—	2	2	no	—
174	#340	C₂²×C₇	1	2	yes	—
175	#336	C₂²×C₇	1	2	yes	—
176	C₂³×C₇	—	2	4	no	—
177	C₂³×C₇	—	4	2	no	—
178	C₂³×C₇	—	4	2	no	—
179	C₂³×C₇	—	4	2	no	—
180	C₂³×C₇	—	4	2	no	—
181	C₂³×C₇	—	4	2	no	—
182	C₂³×C₇	—	4	2	no	—
183	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
184	C₇×Q₈	—	2	4	no	—
185	C₇×Q₈	—	2	4	no	—
186	C₇×Q₈	—	4	2	no	—
187	C₇×Q₈	—	4	2	no	—
188	C₇×D₄	—	2	4	no	—
189	C₇×D₄	—	2	4	no	—
190	C₇×D₄	—	4	2	no	—
191	C₇×D₄	—	4	2	no	—
192	C₂×C₄×C₇	—	2	1	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	4	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	2	4	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	—	4	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	—	4	2	no	—
210	C₂×C₄×C₇	—	4	2	no	—
211	C₂×C₄×C₇	—	8	8	no	—
212	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂²×D₄	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	H(5,𝔽₂)	1	1	yes	characteristic
220	C₇×C₈	—	2	2	no	—
221	C₇×C₈	—	4	2	no	—
222	C₇×C₈	C₄×D₄	1	4	yes	—
223	C₂²×Q₈	C₂³×C₇	1	2	yes	—
224	C₂²×D₄	C₂³×C₇	1	2	yes	—
225	C₂³×C₄	—	2	2	no	—
226	C₂×Q₁₆	—	4	1	no	—
227	C₂×Q₁₆	—	4	1	no	—
228	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
229	C₂×SD₁₆	—	2	4	no	—
230	C₂×SD₁₆	—	2	4	no	—
231	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
232	C₂×D₈	—	4	1	no	—
233	C₂×D₈	—	4	1	no	—
234	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
235	C₂²×C₈	C₂³×C₇	1	2	yes	—
236	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
238	#124	—	2	4	no	—
239	#124	C₂×C₄×C₇	1	8	yes	complemented
240	C₄×Q₈	—	2	4	no	—
241	C₄×Q₈	—	4	2	no	—
242	C₄×D₄	—	2	4	no	—
243	C₄×D₄	—	4	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	C₂³×C₇	1	2	yes	—
257	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
258	#107	—	2	2	no	—
259	#107	C₇×D₄	1	4	yes	—
260	C₄⋊C₈	—	2	2	no	—
261	#103	—	2	4	no	—
262	#103	—	4	2	no	—
263	#102	—	2	4	no	—
264	#102	—	4	2	no	—
265	#97	—	2	4	no	—
266	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	C₇×D₄	1	2	yes	—
271	C₂²×C₇	—	4	4	no	—
272	C₂²×C₇	—	4	4	no	—
273	C₂²×C₇	—	4	4	no	—
274	C₂²×C₇	—	8	2	no	—
275	C₂²×C₇	—	8	2	no	—
276	C₂²×C₇	—	8	2	no	—
277	C₂²×C₇	—	8	2	no	—
278	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₇	D₄²	1	1	yes	characteristic
280	C₂²×C₇	#550	1	1	yes	characteristic
281	C₂²×C₇	#575	1	1	yes	characteristic
282	C₂²×C₇	#575	1	1	yes	characteristic
283	C₂²×C₇	#576	1	1	yes	characteristic
284	C₂²×C₇	#578	1	1	yes	characteristic
285	C₄×C₇	—	2	2	no	—
286	C₄×C₇	—	2	2	no	—
287	C₄×C₇	—	4	4	no	—
288	C₄×C₇	—	4	2	no	—
289	C₄×C₇	—	4	4	no	—
290	C₄×C₇	—	4	2	no	—
291	C₄×C₇	—	8	2	no	—
292	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
293	C₄×C₇	#518	1	1	yes	characteristic
294	C₄×C₇	#550	1	1	yes	characteristic
295	C₄×C₇	#559	1	1	yes	characteristic
296	C₂⁴	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
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	C₂²×C₄×C₇	1	4	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	8	2	no	—
315	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
317	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
320	Q₁₆	—	4	4	no	—
321	SD₁₆	—	2	16	no	—
322	D₈	—	4	4	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
329	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
330	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
331	C₂×C₈	C₇×#41	1	2	yes	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	8	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	4	4	no	—
347	C₄²	—	8	2	no	—
348	C₄²	C₂²×C₄×C₇	1	2	yes	—
349	C₄²	C₇×#41	1	2	yes	—
350	C₂×C₇	—	8	4	no	—
351	C₂×C₇	#2366	1	1	yes	characteristic
352	C₂×C₇	#2943	1	1	yes	characteristic
353	C₂×C₇	#2951	1	1	yes	characteristic
354	C₂×C₇	#3273	1	1	yes	characteristic
355	C₂×C₇	#3277	1	1	yes	characteristic
356	C₂×C₇	#3402	1	1	yes	characteristic
357	C₂×C₇	#3403	1	1	yes	characteristic
358	C₂³	—	2	4	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	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	—	4	2	no	—
393	C₂×C₄	—	8	8	no	—
394	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
395	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
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	C₇×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	2	no	—
404	C₈	C₄×C₇×D₄	1	4	yes	—
405	C₇	#23191	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	4	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
414	C₂²	C₇×D₄²	1	1	yes	characteristic
415	C₂²	C₇×#550	1	1	yes	characteristic
416	C₂²	C₇×#575	1	1	yes	characteristic
417	C₂²	C₇×#575	1	1	yes	characteristic
418	C₂²	C₇×#576	1	1	yes	characteristic
419	C₂²	C₇×#578	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	2	no	—
427	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
428	C₄	C₇×#518	1	1	yes	characteristic
429	C₄	C₇×#550	1	1	yes	characteristic
430	C₄	C₇×#559	1	1	yes	characteristic
431	C₂	—	8	4	no	—
432	C₂	C₇×#2366	1	1	yes	characteristic
433	C₂	C₇×#2943	1	1	yes	characteristic
434	C₂	C₇×#2951	1	1	yes	characteristic
435	C₂	C₇×#3273	1	1	yes	characteristic
436	C₂	C₇×#3277	1	1	yes	characteristic
437	C₂	C₇×#3402	1	1	yes	characteristic
438	C₂	C₇×#3403	1	1	yes	characteristic

	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
2. C₂×C₇×#440	C₂	semidirect
3. C₇×#2367	C₂	semidirect
4. C₇×#1983	C₂	semidirect
5. C₇×#1973	C₂	semidirect
7. C₇×#1878	C₂	semidirect
8. C₄×C₇×#107	C₂	semidirect
9. C₇×#1770	C₂	semidirect
16. C₇×#495	C₄	semidirect
37. #23191	C₇	direct (N × H)
43. C₂×C₇×Q₁₆	C₂×C₄	semidirect
46. C₂×C₇×SD₁₆	C₂×C₄	semidirect
54. C₇×#124	C₂×C₄	semidirect
81. C₄×C₇×C₈	C₂×C₄	semidirect
87. C₂×#440	C₂×C₇	semidirect
88. #2367	C₂×C₇	semidirect
89. #1983	C₂×C₇	semidirect
90. #1973	C₂×C₇	semidirect
92. #1878	C₂×C₇	semidirect
93. C₄×#107	C₂×C₇	semidirect
94. #1770	C₂×C₇	semidirect
155. #495	C₄×C₇	semidirect
228. C₂×Q₁₆	C₂×C₄×C₇	semidirect
231. C₂×SD₁₆	C₂×C₄×C₇	semidirect
239. #124	C₂×C₄×C₇	semidirect
266. C₄×C₈	C₂×C₄×C₇	semidirect
405. C₇	#23191	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×#440	2
C₇×#2367	2
C₇×#1983	2
C₇×#1973	2
C₇×#1879	2
C₇×#1878	2
C₄×C₇×#107	2
C₇×#1770	2
#23191	7

Subgroups — C7×#23191 #13200407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23191 #13200407