Subgroups — C₇×#22806 #13200022

Order 1792.

814 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₇×#2357	C₂	1	1	yes	maximal, characteristic
3	C₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1968	C₂	1	2	yes	maximal
5	C₇×#1928	C₂	1	2	yes	maximal, complemented
6	C₇×#1925	C₂	1	2	yes	maximal
7	C₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1804	C₂	1	1	yes	maximal, characteristic
10	C₄×C₇×#106	C₂	1	2	yes	maximal, complemented
11	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₄×C₇×SD₁₆	C₄	1	8	yes	complemented
16	C₂×C₇×#107	C₂²	1	2	yes	—
17	C₂×C₇×#106	C₂²	1	2	yes	—
18	C₂×C₇×#106	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#103	C₂²	1	2	yes	—
21	C₂×C₇×#103	C₂²	1	1	yes	characteristic
22	C₂×C₇×#102	C₂²	1	2	yes	—
23	C₂×C₇×#102	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₇×#391	C₂²	1	2	yes	—
27	C₇×#390	C₂²	1	2	yes	—
28	C₇×#388	—	2	2	no	—
29	C₇×#387	—	2	2	no	—
30	C₇×#383	—	2	1	no	—
31	C₇×#382	C₂²	1	1	yes	characteristic
32	C₇×#382	C₂²	1	1	yes	characteristic
33	C₇×#381	—	2	1	no	—
34	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
38	C₇×#376	—	2	1	no	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	#22806	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇	—	2	1	no	—
46	C₂×C₇×SD₁₆	—	2	2	no	—
47	C₂×C₇×SD₁₆	—	2	2	no	—
48	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₄×C₇×Q₈	—	2	2	no	—
53	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
54	C₄×C₇×D₄	—	2	2	no	—
55	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
56	C₂×C₇×C₄⋊C₄	—	2	1	no	—
57	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
58	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₄²×C₇	—	2	1	no	—
66	C₂×C₄²×C₇	—	2	2	no	—
67	C₂×C₄²×C₇	—	2	2	no	—
68	C₂×C₄²×C₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₇×#107	—	4	2	no	—
71	C₇×#106	—	2	4	no	—
72	C₇×#106	C₂×C₄	1	4	yes	—
73	C₇×C₄⋊C₈	—	2	2	no	—
74	C₇×#103	—	4	2	no	—
75	C₇×#103	C₂×C₄	1	4	yes	—
76	C₇×#102	—	4	2	no	—
77	C₇×#102	C₂×C₄	1	4	yes	—
78	C₄×C₇×C₈	—	2	4	no	—
79	C₄×C₇×C₈	C₂×C₄	1	4	yes	—
80	C₇×#95	—	2	1	no	—
81	C₇×#95	—	2	2	no	—
82	C₇×#95	—	2	1	no	—
83	C₇×#95	—	2	2	no	—
84	C₇×#95	—	2	2	no	—
85	C₇×#95	—	2	1	no	—
86	C₇×#95	—	2	1	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	D₄	1	1	yes	characteristic
89	C₇×#95	D₄	1	1	yes	characteristic
90	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
91	#2357	C₂×C₇	1	1	yes	characteristic
92	#2356	C₂×C₇	1	1	yes	characteristic, complemented
93	#1968	C₂×C₇	1	2	yes	—
94	#1928	C₂×C₇	1	2	yes	complemented
95	#1925	C₂×C₇	1	2	yes	—
96	#1846	C₂×C₇	1	1	yes	characteristic, complemented
97	#1805	C₂×C₇	1	1	yes	characteristic, complemented
98	#1804	C₂×C₇	1	1	yes	characteristic
99	C₄×#106	C₂×C₇	1	2	yes	complemented
100	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
101	C₂⁴×C₇	—	2	1	no	—
102	C₂×C₇×Q₈	—	2	1	no	—
103	C₂×C₇×Q₈	—	2	1	no	—
104	C₂×C₇×Q₈	—	2	1	no	—
105	C₂×C₇×Q₈	—	2	1	no	—
106	C₂×C₇×Q₈	—	2	1	no	—
107	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
108	C₂×C₇×D₄	—	2	1	no	—
109	C₂×C₇×D₄	—	2	1	no	—
110	C₂×C₇×D₄	—	2	1	no	—
111	C₂×C₇×D₄	—	2	1	no	—
112	C₂×C₇×D₄	—	2	1	no	—
113	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	—	2	1	no	—
116	C₂²×C₄×C₇	—	2	1	no	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	8	2	no	—
121	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
126	C₇×SD₁₆	—	2	8	no	—
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	2	2	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₇×C₈	#41	1	2	yes	—
135	C₂×C₇×C₈	#41	1	2	yes	—
136	C₇×C₄⋊C₄	—	2	4	no	—
137	C₇×C₄⋊C₄	—	2	4	no	—
138	C₇×C₄⋊C₄	—	2	1	no	—
139	C₇×C₄⋊C₄	—	2	1	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	C₂²×C₄	1	2	yes	—
145	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
146	C₇×C₂²⋊C₄	—	2	4	no	—
147	C₇×C₂²⋊C₄	—	4	4	no	—
148	C₇×C₂²⋊C₄	—	8	2	no	—
149	C₄²×C₇	—	2	4	no	—
150	C₄²×C₇	—	2	2	no	—
151	C₄²×C₇	—	2	2	no	—
152	C₄²×C₇	—	4	4	no	—
153	C₄²×C₇	—	8	2	no	—
154	C₄²×C₇	C₂²×C₄	1	2	yes	—
155	C₄²×C₇	#41	1	2	yes	—
156	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
157	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
158	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
159	C₄×SD₁₆	C₄×C₇	1	8	yes	complemented
160	C₂×#107	C₂²×C₇	1	2	yes	—
161	C₂×#106	C₂²×C₇	1	2	yes	—
162	C₂×#106	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
164	C₂×#103	C₂²×C₇	1	2	yes	—
165	C₂×#103	C₂²×C₇	1	1	yes	characteristic
166	C₂×#102	C₂²×C₇	1	2	yes	—
167	C₂×#102	C₂²×C₇	1	1	yes	characteristic
168	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
169	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
170	#391	C₂²×C₇	1	2	yes	—
171	#390	C₂²×C₇	1	2	yes	—
172	#388	—	2	2	no	—
173	#387	—	2	2	no	—
174	#383	—	2	1	no	—
175	#382	C₂²×C₇	1	1	yes	characteristic
176	#382	C₂²×C₇	1	1	yes	characteristic
177	#381	—	2	1	no	—
178	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
179	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
180	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	—	2	1	no	—
182	#376	—	2	1	no	—
183	#340	C₂²×C₇	1	2	yes	—
184	#340	C₂²×C₇	1	2	yes	—
185	#336	C₂²×C₇	1	2	yes	—
186	C₂³×C₇	—	2	2	no	—
187	C₂³×C₇	—	4	1	no	—
188	C₂³×C₇	—	4	1	no	—
189	C₂³×C₇	—	4	2	no	—
190	C₂³×C₇	—	4	2	no	—
191	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
192	C₇×Q₈	—	2	2	no	—
193	C₇×Q₈	—	2	2	no	—
194	C₇×Q₈	—	4	1	no	—
195	C₇×Q₈	—	4	1	no	—
196	C₇×D₄	—	2	2	no	—
197	C₇×D₄	—	2	2	no	—
198	C₇×D₄	—	4	1	no	—
199	C₇×D₄	—	4	1	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	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	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	—	4	1	no	—
211	C₂×C₄×C₇	—	4	1	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	—	8	4	no	—
221	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
222	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₇	#135	1	4	yes	—
224	C₂×C₄×C₇	C₂³×C₄	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	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
230	C₇×C₈	—	2	2	no	—
231	C₇×C₈	—	4	2	no	—
232	C₇×C₈	#117	1	4	yes	—
233	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
234	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
235	C₂³×C₄	—	2	1	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
239	C₂²×C₈	C₂³×C₇	1	2	yes	—
240	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
242	C₄×Q₈	—	2	2	no	—
243	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	C₂³×C₇	1	2	yes	—
259	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
260	#107	—	4	2	no	—
261	#106	—	2	4	no	—
262	#106	C₂×C₄×C₇	1	4	yes	—
263	C₄⋊C₈	—	2	2	no	—
264	#103	—	4	2	no	—
265	#103	C₂×C₄×C₇	1	4	yes	—
266	#102	—	4	2	no	—
267	#102	C₂×C₄×C₇	1	4	yes	—
268	C₄×C₈	—	2	4	no	—
269	C₄×C₈	C₂×C₄×C₇	1	4	yes	—
270	#95	—	2	1	no	—
271	#95	—	2	2	no	—
272	#95	—	2	1	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	#95	—	2	2	no	—
278	#95	C₇×D₄	1	1	yes	characteristic
279	#95	C₇×D₄	1	1	yes	characteristic
280	C₂²×C₇	—	4	2	no	—
281	C₂²×C₇	—	4	2	no	—
282	C₂²×C₇	—	4	2	no	—
283	C₂²×C₇	—	8	2	no	—
284	C₂²×C₇	—	8	2	no	—
285	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂²×C₇	#547	1	1	yes	characteristic
287	C₂²×C₇	#550	1	1	yes	characteristic
288	C₂²×C₇	C₂×#135	1	2	yes	—
289	C₂²×C₇	#577	1	2	yes	—
290	C₄×C₇	—	2	4	no	—
291	C₄×C₇	—	2	2	no	—
292	C₄×C₇	—	2	2	no	—
293	C₄×C₇	—	4	2	no	—
294	C₄×C₇	—	4	2	no	—
295	C₄×C₇	—	4	2	no	—
296	C₄×C₇	—	4	2	no	—
297	C₄×C₇	—	8	2	no	—
298	C₄×C₇	—	8	2	no	—
299	C₄×C₇	C₂×#117	1	1	yes	characteristic
300	C₄×C₇	#520	1	1	yes	characteristic
301	C₄×C₇	#555	1	1	yes	characteristic
302	C₄×C₇	#556	1	1	yes	characteristic
303	C₂⁴	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	8	2	no	—
323	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
324	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
328	SD₁₆	—	2	8	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
335	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
336	C₂×C₈	C₇×#41	1	2	yes	—
337	C₂×C₈	C₇×#41	1	2	yes	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
347	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	8	2	no	—
351	C₄²	—	2	4	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	4	4	no	—
355	C₄²	—	8	2	no	—
356	C₄²	C₂²×C₄×C₇	1	2	yes	—
357	C₄²	C₇×#41	1	2	yes	—
358	C₂×C₇	—	8	2	no	—
359	C₂×C₇	#2354	1	1	yes	characteristic
360	C₂×C₇	C₄×#135	1	1	yes	characteristic
361	C₂×C₇	#2949	1	1	yes	characteristic
362	C₂×C₇	#3337	1	2	yes	—
363	C₂×C₇	#3394	1	2	yes	—
364	C₂³	—	2	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	4	1	no	—
373	Q₈	—	4	1	no	—
374	D₄	—	2	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	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	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	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	—	4	2	no	—
398	C₂×C₄	—	8	4	no	—
399	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
400	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
401	C₂×C₄	C₇×#135	1	4	yes	—
402	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
403	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
404	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
405	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
406	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	4	2	no	—
410	C₈	C₇×#117	1	4	yes	—
411	C₇	#22806	1	1	yes	characteristic, direct product factor, Sylow
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
418	C₂²	C₇×#547	1	1	yes	characteristic
419	C₂²	C₇×#550	1	1	yes	characteristic
420	C₂²	C₂×C₇×#135	1	2	yes	—
421	C₂²	C₇×#577	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	4	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	C₂×C₇×#117	1	1	yes	characteristic
432	C₄	C₇×#520	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	C₄×C₇×#135	1	1	yes	characteristic
438	C₂	C₇×#2949	1	1	yes	characteristic
439	C₂	C₇×#3337	1	2	yes	—
440	C₂	C₇×#3394	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×D₄	C₂³
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. C₇×#2356	C₂	semidirect
5. C₇×#1928	C₂	semidirect
7. C₇×#1846	C₂	semidirect
8. C₇×#1805	C₂	semidirect
10. C₄×C₇×#106	C₂	semidirect
11. C₇×C₈×C₄⋊C₄	C₂	semidirect
15. C₄×C₇×SD₁₆	C₄	semidirect
42. #22806	C₇	direct (N × H)
92. #2356	C₂×C₇	semidirect
94. #1928	C₂×C₇	semidirect
96. #1846	C₂×C₇	semidirect
97. #1805	C₂×C₇	semidirect
99. C₄×#106	C₂×C₇	semidirect
100. C₈×C₄⋊C₄	C₂×C₇	semidirect
159. C₄×SD₁₆	C₄×C₇	semidirect
411. C₇	#22806	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×SD₁₆	2
C₇×#2357	2
C₇×#2356	2
C₇×#1968	2
C₇×#1928	2
C₇×#1925	2
C₇×#1846	2
C₇×#1805	2
C₇×#1804	2
C₄×C₇×#106	2
C₇×C₈×C₄⋊C₄	2
#22806	7

Subgroups — C7×#22806 #13200022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22806 #13200022