Subgroups — C₇×#23028 #13200244

Order 1792.

970 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₇×#106	C₂	1	1	yes	maximal, characteristic
4	C₇×#2360	C₂	1	2	yes	maximal
5	C₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1927	C₂	1	2	yes	maximal, complemented
8	C₇×#1872	C₂	1	2	yes	maximal
9	C₇×#1865	C₂	1	2	yes	maximal, complemented
10	C₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1752	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
16	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
17	C₇×#467	C₄	1	8	yes	complemented
18	C₇×#441	—	2	4	no	—
19	C₂×C₇×#107	C₂²	1	1	yes	characteristic
20	C₂×C₇×#106	—	2	4	no	—
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	2	yes	—
23	C₂×C₇×#106	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×#103	C₂²	1	2	yes	—
26	C₂×C₇×#103	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×#97	C₂²	1	1	yes	characteristic
29	C₂×C₇×#97	C₂²	1	1	yes	characteristic
30	C₇×#391	C₂²	1	2	yes	—
31	C₇×#389	—	2	2	no	—
32	C₇×#389	C₂²	1	2	yes	—
33	C₇×#387	—	2	2	no	—
34	C₇×#385	—	2	2	no	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₇×C₂²⋊C₄	—	2	2	no	—
37	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	1	yes	characteristic
42	#23028	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₇	—	2	2	no	—
45	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	C₂²×C₇×C₈	—	2	2	no	—
50	C₂²×C₇×C₈	—	2	2	no	—
51	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₇×C₂²⋊Q₈	—	2	4	no	—
57	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
58	C₄×C₇×Q₈	—	2	4	no	—
59	C₄×C₇×Q₈	—	4	2	no	—
60	C₂×C₇×C₄⋊C₄	—	2	2	no	—
61	C₂×C₇×C₄⋊C₄	—	2	4	no	—
62	C₂×C₇×C₄⋊C₄	—	2	2	no	—
63	C₂×C₇×C₄⋊C₄	—	2	2	no	—
64	C₂×C₇×C₄⋊C₄	—	2	2	no	—
65	C₂×C₇×C₄⋊C₄	—	4	2	no	—
66	C₂×C₇×C₄⋊C₄	C₂³	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	D₄	1	2	yes	—
71	C₂×C₄²×C₇	—	2	2	no	—
72	C₂×C₄²×C₇	—	2	2	no	—
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₇×#107	C₂×C₄	1	4	yes	complemented
76	C₇×#106	—	2	2	no	—
77	C₇×#106	—	2	4	no	—
78	C₇×#106	D₄	1	4	yes	—
79	C₇×#103	—	2	4	no	—
80	C₇×#103	—	4	2	no	—
81	C₇×#103	C₂×C₄	1	8	yes	complemented
82	C₇×C₂²⋊C₈	—	2	2	no	—
83	C₇×#97	—	2	2	no	—
84	C₇×#97	—	2	2	no	—
85	C₇×#95	—	2	2	no	—
86	C₇×#95	—	2	2	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	—	2	2	no	—
89	C₇×#95	D₄	1	2	yes	—
90	C₂×#467	C₂×C₇	1	1	yes	characteristic
91	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
92	C₂²×#106	C₂×C₇	1	1	yes	characteristic
93	#2360	C₂×C₇	1	2	yes	—
94	#1971	C₂×C₇	1	1	yes	characteristic, complemented
95	#1943	C₂×C₇	1	1	yes	characteristic, complemented
96	#1927	C₂×C₇	1	2	yes	complemented
97	#1872	C₂×C₇	1	2	yes	—
98	#1865	C₂×C₇	1	2	yes	complemented
99	#1776	C₂×C₇	1	1	yes	characteristic, complemented
100	#1752	C₂×C₇	1	1	yes	characteristic
101	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
106	C₂×C₇×Q₈	—	2	2	no	—
107	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₇	—	2	1	no	—
109	C₂²×C₄×C₇	—	2	1	no	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	1	no	—
112	C₂²×C₄×C₇	—	2	2	no	—
113	C₂²×C₄×C₇	—	2	2	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	4	4	no	—
117	C₂²×C₄×C₇	—	4	4	no	—
118	C₂²×C₄×C₇	—	8	2	no	—
119	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	#41	1	2	yes	—
124	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
125	C₇×Q₁₆	—	2	8	no	—
126	C₂×C₇×C₈	—	2	1	no	—
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	8	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	1	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	C₂²×C₄	1	2	yes	—
136	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₇×C₈	#41	1	2	yes	—
139	C₇×C₄⋊C₄	—	2	8	no	—
140	C₇×C₄⋊C₄	—	2	2	no	—
141	C₇×C₄⋊C₄	—	2	2	no	—
142	C₇×C₄⋊C₄	—	2	2	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	4	4	no	—
145	C₇×C₄⋊C₄	—	4	4	no	—
146	C₇×C₄⋊C₄	—	8	2	no	—
147	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
148	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
149	C₇×C₂²⋊C₄	—	2	8	no	—
150	C₇×C₂²⋊C₄	—	2	4	no	—
151	C₄²×C₇	—	2	1	no	—
152	C₄²×C₇	—	2	1	no	—
153	C₄²×C₇	—	2	1	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	—	4	4	no	—
156	C₄²×C₇	—	8	2	no	—
157	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
158	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
159	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
160	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
161	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
162	#467	C₄×C₇	1	8	yes	complemented
163	#441	—	2	4	no	—
164	C₂×#107	C₂²×C₇	1	1	yes	characteristic
165	C₂×#106	—	2	4	no	—
166	C₂×#106	C₂²×C₇	1	2	yes	—
167	C₂×#106	C₂²×C₇	1	1	yes	characteristic
168	C₂×#106	C₂²×C₇	1	1	yes	characteristic
169	C₂×#103	C₂²×C₇	1	2	yes	—
170	C₂×#103	C₂²×C₇	1	2	yes	—
171	C₂×#103	C₂²×C₇	1	2	yes	—
172	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
173	C₂×#97	C₂²×C₇	1	1	yes	characteristic
174	C₂×#97	C₂²×C₇	1	1	yes	characteristic
175	#391	C₂²×C₇	1	2	yes	—
176	#389	—	2	2	no	—
177	#389	C₂²×C₇	1	2	yes	—
178	#387	—	2	2	no	—
179	#385	—	2	2	no	—
180	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
181	C₄×C₂²⋊C₄	—	2	2	no	—
182	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
183	#340	C₂²×C₇	1	2	yes	—
184	#340	C₂²×C₇	1	2	yes	—
185	#336	C₂²×C₇	1	1	yes	characteristic
186	#336	C₂²×C₇	1	1	yes	characteristic
187	C₂³×C₇	—	2	1	no	—
188	C₂³×C₇	—	2	1	no	—
189	C₂³×C₇	—	2	2	no	—
190	C₂³×C₇	C₄×D₄	1	2	yes	—
191	C₂³×C₇	#137	1	4	yes	—
192	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
193	C₇×Q₈	—	2	4	no	—
194	C₇×Q₈	—	2	4	no	—
195	C₇×Q₈	—	4	2	no	—
196	C₇×Q₈	—	4	2	no	—
197	C₂×C₄×C₇	—	2	1	no	—
198	C₂×C₄×C₇	—	2	1	no	—
199	C₂×C₄×C₇	—	2	2	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	4	no	—
204	C₂×C₄×C₇	—	2	4	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	4	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	2	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	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	—	4	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	—	8	8	no	—
222	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
229	C₇×C₈	—	2	2	no	—
230	C₇×C₈	—	4	1	no	—
231	C₇×C₈	—	4	1	no	—
232	C₇×C₈	C₄×D₄	1	4	yes	—
233	C₂²×Q₈	C₂³×C₇	1	2	yes	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
236	C₂×Q₁₆	—	2	2	no	—
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
242	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	4	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	4	2	no	—
256	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
265	#107	C₂×C₄×C₇	1	4	yes	complemented
266	#106	—	2	2	no	—
267	#106	—	2	4	no	—
268	#106	C₇×D₄	1	4	yes	—
269	#103	—	2	4	no	—
270	#103	—	4	2	no	—
271	#103	C₂×C₄×C₇	1	8	yes	complemented
272	C₂²⋊C₈	—	2	2	no	—
273	#97	—	2	2	no	—
274	#97	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	C₇×D₄	1	2	yes	—
280	C₂²×C₇	—	2	4	no	—
281	C₂²×C₇	—	2	2	no	—
282	C₂²×C₇	—	2	2	no	—
283	C₂²×C₇	—	2	4	no	—
284	C₂²×C₇	#441	1	4	yes	complemented
285	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂²×C₇	D₄²	1	1	yes	characteristic
287	C₂²×C₇	#547	1	1	yes	characteristic
288	C₂²×C₇	C₂×#137	1	2	yes	—
289	C₂²×C₇	#577	1	2	yes	—
290	C₄×C₇	—	2	2	no	—
291	C₄×C₇	—	4	2	no	—
292	C₄×C₇	—	4	4	no	—
293	C₄×C₇	—	4	4	no	—
294	C₄×C₇	—	4	2	no	—
295	C₄×C₇	—	4	4	no	—
296	C₄×C₇	—	8	2	no	—
297	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
298	C₄×C₇	#520	1	1	yes	characteristic
299	C₄×C₇	#548	1	1	yes	characteristic
300	C₄×C₇	#553	1	1	yes	characteristic
301	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	8	2	no	—
319	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
320	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
321	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
322	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₇×#41	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
325	Q₁₆	—	2	8	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	8	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
336	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
337	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
338	C₂×C₈	C₇×#41	1	2	yes	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	8	2	no	—
347	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
348	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	4	4	no	—
356	C₄²	—	8	2	no	—
357	C₂×C₇	—	2	4	no	—
358	C₂×C₇	#2361	1	1	yes	characteristic
359	C₂×C₇	C₂×#441	1	1	yes	characteristic
360	C₂×C₇	#2952	1	1	yes	characteristic
361	C₂×C₇	#3266	1	2	yes	—
362	C₂×C₇	#3344	1	2	yes	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	2	no	—
366	C₂³	C₄×C₇×D₄	1	2	yes	—
367	C₂³	C₇×#137	1	4	yes	—
368	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
369	Q₈	—	2	4	no	—
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	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	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	8	no	—
398	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
399	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
402	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
403	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	1	no	—
408	C₈	C₄×C₇×D₄	1	4	yes	—
409	C₇	#23028	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	2	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	2	no	—
414	C₂²	C₇×#441	1	4	yes	complemented
415	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
416	C₂²	C₇×D₄²	1	1	yes	characteristic
417	C₂²	C₇×#547	1	1	yes	characteristic
418	C₂²	C₂×C₇×#137	1	2	yes	—
419	C₂²	C₇×#577	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	4	4	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×#520	1	1	yes	characteristic
429	C₄	C₇×#548	1	1	yes	characteristic
430	C₄	C₇×#553	1	1	yes	characteristic
431	C₂	—	2	4	no	—
432	C₂	C₇×#2361	1	1	yes	characteristic
433	C₂	C₂×C₇×#441	1	1	yes	characteristic
434	C₂	C₇×#2952	1	1	yes	characteristic
435	C₂	C₇×#3266	1	2	yes	—
436	C₂	C₇×#3344	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	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#441	C₂	semidirect
5. C₇×#1971	C₂	semidirect
6. C₇×#1943	C₂	semidirect
7. C₇×#1927	C₂	semidirect
9. C₇×#1865	C₂	semidirect
10. C₇×#1776	C₂	semidirect
17. C₇×#467	C₄	semidirect
42. #23028	C₇	direct (N × H)
48. C₂×C₇×Q₁₆	C₂×C₄	semidirect
75. C₇×#107	C₂×C₄	semidirect
81. C₇×#103	C₂×C₄	semidirect
91. C₂×#441	C₂×C₇	semidirect
94. #1971	C₂×C₇	semidirect
95. #1943	C₂×C₇	semidirect
96. #1927	C₂×C₇	semidirect
98. #1865	C₂×C₇	semidirect
99. #1776	C₂×C₇	semidirect
162. #467	C₄×C₇	semidirect
238. C₂×Q₁₆	C₂×C₄×C₇	semidirect
265. #107	C₂×C₄×C₇	semidirect
271. #103	C₂×C₄×C₇	semidirect
284. C₂²×C₇	#441	semidirect
409. C₇	#23028	direct (N × H)
414. C₂²	C₇×#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#467	2
C₂×C₇×#441	2
C₂²×C₇×#106	2
C₇×#2360	2
C₇×#1971	2
C₇×#1943	2
C₇×#1927	2
C₇×#1872	2
C₇×#1865	2
C₇×#1776	2
C₇×#1752	2
#23028	7

Subgroups — C7×#23028 #13200244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23028 #13200244