Subgroups — C₇×#23186 #13200402

Order 1792.

1038 conjugacy classes of subgroups.

The subgroup lattice has 490 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×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic
4	C₇×#2367	C₂	1	2	yes	maximal, complemented
5	C₇×#1983	C₂	1	2	yes	maximal, complemented
6	C₇×#1970	C₂	1	1	yes	maximal, characteristic
7	C₇×#1969	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×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×C₄⋊C₄	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	C₄×C₇×Q₁₆	—	2	4	no	—
20	C₄×C₇×D₈	—	2	4	no	—
21	C₂×C₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₇×#107	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×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	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	#23186	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	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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×C₇×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₇	—	2	2	no	—
76	C₂×C₄²×C₇	—	2	2	no	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×#107	—	2	2	no	—
81	C₇×#107	D₄	1	4	yes	—
82	C₇×C₄⋊C₈	—	2	2	no	—
83	C₇×#103	—	2	4	no	—
84	C₇×#103	—	4	2	no	—
85	C₇×#102	—	2	4	no	—
86	C₇×#102	—	4	2	no	—
87	C₄×C₇×C₈	—	2	2	no	—
88	C₄×C₇×C₈	—	2	2	no	—
89	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
90	C₇×#95	—	2	2	no	—
91	C₇×#95	—	2	2	no	—
92	C₇×#95	—	2	2	no	—
93	C₇×#95	D₄	1	1	yes	characteristic
94	C₇×#95	D₄	1	1	yes	characteristic
95	C₂×#495	C₂×C₇	1	1	yes	characteristic
96	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
97	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic
98	#2367	C₂×C₇	1	2	yes	complemented
99	#1983	C₂×C₇	1	2	yes	complemented
100	#1970	C₂×C₇	1	1	yes	characteristic
101	#1969	C₂×C₇	1	1	yes	characteristic, complemented
102	#1880	C₂×C₇	1	2	yes	complemented
103	#1877	C₂×C₇	1	2	yes	complemented
104	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
105	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
106	C₂⁴×C₇	—	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	—	2	2	no	—
111	C₂×C₇×Q₈	—	2	2	no	—
112	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
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	—	2	2	no	—
117	C₂×C₇×D₄	—	2	2	no	—
118	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	4	4	no	—
123	C₂²×C₄×C₇	—	4	4	no	—
124	C₂²×C₄×C₇	—	8	2	no	—
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
132	C₇×Q₁₆	—	2	8	no	—
133	C₇×SD₁₆	—	4	8	no	—
134	C₇×D₈	—	2	8	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	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₇×C₈	#41	1	2	yes	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	2	2	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	4	4	no	—
153	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
154	C₇×C₂²⋊C₄	—	2	8	no	—
155	C₇×C₂²⋊C₄	—	2	8	no	—
156	C₇×C₂²⋊C₄	—	4	4	no	—
157	C₇×C₂²⋊C₄	—	4	4	no	—
158	C₇×C₂²⋊C₄	—	8	2	no	—
159	C₄²×C₇	—	2	1	no	—
160	C₄²×C₇	—	2	1	no	—
161	C₄²×C₇	—	2	1	no	—
162	C₄²×C₇	—	2	1	no	—
163	C₄²×C₇	—	4	4	no	—
164	C₄²×C₇	—	8	2	no	—
165	C₄²×C₇	C₂²×C₄	1	2	yes	—
166	C₄²×C₇	#41	1	2	yes	—
167	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
168	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
169	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
170	C₂×#124	C₂²×C₇	1	2	yes	—
171	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
172	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
173	#495	C₄×C₇	1	8	yes	complemented
174	C₄×Q₁₆	—	2	4	no	—
175	C₄×D₈	—	2	4	no	—
176	C₂×#107	C₂²×C₇	1	1	yes	characteristic
177	C₂×#107	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×#103	C₂²×C₇	1	2	yes	—
180	C₂×#103	C₂²×C₇	1	2	yes	—
181	C₂×#102	C₂²×C₇	1	2	yes	—
182	C₂×#102	C₂²×C₇	1	2	yes	—
183	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
186	#391	C₂²×C₇	1	2	yes	—
187	#390	C₂²×C₇	1	2	yes	—
188	#388	—	2	2	no	—
189	#388	—	2	2	no	—
190	#385	—	2	2	no	—
191	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
192	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
193	C₄×C₂²⋊C₄	—	2	2	no	—
194	#340	C₂²×C₇	1	2	yes	—
195	#336	C₂²×C₇	1	1	yes	characteristic
196	#336	C₂²×C₇	1	1	yes	characteristic
197	C₂³×C₇	—	2	4	no	—
198	C₂³×C₇	—	4	2	no	—
199	C₂³×C₇	—	4	2	no	—
200	C₂³×C₇	—	4	2	no	—
201	C₂³×C₇	—	4	2	no	—
202	C₂³×C₇	—	4	2	no	—
203	C₂³×C₇	—	4	2	no	—
204	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
205	C₇×Q₈	—	2	4	no	—
206	C₇×Q₈	—	2	4	no	—
207	C₇×Q₈	—	4	2	no	—
208	C₇×Q₈	—	4	2	no	—
209	C₇×D₄	—	2	4	no	—
210	C₇×D₄	—	2	4	no	—
211	C₇×D₄	—	4	2	no	—
212	C₇×D₄	—	4	2	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	4	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	4	no	—
225	C₂×C₄×C₇	—	2	1	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	1	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	4	2	no	—
231	C₂×C₄×C₇	—	4	2	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	4	2	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	8	8	no	—
237	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
239	C₂×C₄×C₇	#135	1	2	yes	—
240	C₂×C₄×C₇	#135	1	2	yes	—
241	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
247	C₇×C₈	—	2	2	no	—
248	C₇×C₈	—	4	1	no	—
249	C₇×C₈	—	4	1	no	—
250	C₇×C₈	C₄×D₄	1	4	yes	—
251	C₂²×Q₈	C₂³×C₇	1	2	yes	—
252	C₂²×D₄	C₂³×C₇	1	2	yes	—
253	C₂³×C₄	—	2	2	no	—
254	C₂×Q₁₆	—	2	2	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
257	C₂×SD₁₆	—	4	2	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
260	C₂×D₈	—	2	2	no	—
261	C₂×D₈	—	2	2	no	—
262	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
263	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
267	#124	—	2	4	no	—
268	#124	C₂×C₄×C₇	1	8	yes	complemented
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	—	4	2	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	4	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
288	#107	—	2	2	no	—
289	#107	C₇×D₄	1	4	yes	—
290	C₄⋊C₈	—	2	2	no	—
291	#103	—	2	4	no	—
292	#103	—	4	2	no	—
293	#102	—	2	4	no	—
294	#102	—	4	2	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	C₇×D₄	1	1	yes	characteristic
302	#95	C₇×D₄	1	1	yes	characteristic
303	C₂²×C₇	—	4	4	no	—
304	C₂²×C₇	—	4	4	no	—
305	C₂²×C₇	—	4	4	no	—
306	C₂²×C₇	—	8	2	no	—
307	C₂²×C₇	—	8	2	no	—
308	C₂²×C₇	—	8	2	no	—
309	C₂²×C₇	—	8	2	no	—
310	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
311	C₂²×C₇	D₄²	1	1	yes	characteristic
312	C₂²×C₇	#550	1	1	yes	characteristic
313	C₂²×C₇	C₂×#135	1	1	yes	characteristic
314	C₂²×C₇	C₂×#135	1	1	yes	characteristic
315	C₂²×C₇	#576	1	1	yes	characteristic
316	C₂²×C₇	#578	1	1	yes	characteristic
317	C₄×C₇	—	2	2	no	—
318	C₄×C₇	—	2	2	no	—
319	C₄×C₇	—	2	2	no	—
320	C₄×C₇	—	2	2	no	—
321	C₄×C₇	—	4	4	no	—
322	C₄×C₇	—	4	1	no	—
323	C₄×C₇	—	4	4	no	—
324	C₄×C₇	—	4	1	no	—
325	C₄×C₇	—	8	2	no	—
326	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
327	C₄×C₇	#518	1	1	yes	characteristic
328	C₄×C₇	#550	1	1	yes	characteristic
329	C₄×C₇	#559	1	1	yes	characteristic
330	C₂⁴	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	8	2	no	—
349	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
356	Q₁₆	—	2	8	no	—
357	SD₁₆	—	4	8	no	—
358	D₈	—	2	8	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
368	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
369	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
370	C₂×C₈	C₇×#41	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	8	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	4	4	no	—
388	C₄²	—	8	2	no	—
389	C₄²	C₂²×C₄×C₇	1	2	yes	—
390	C₄²	C₇×#41	1	2	yes	—
391	C₂×C₇	—	8	4	no	—
392	C₂×C₇	#2366	1	1	yes	characteristic
393	C₂×C₇	C₄×#135	1	1	yes	characteristic
394	C₂×C₇	#2951	1	1	yes	characteristic
395	C₂×C₇	#3280	1	1	yes	characteristic
396	C₂×C₇	#3285	1	1	yes	characteristic
397	C₂×C₇	#3393	1	1	yes	characteristic
398	C₂×C₇	#3396	1	1	yes	characteristic
399	C₂³	—	2	4	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
407	Q₈	—	2	4	no	—
408	Q₈	—	2	4	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	D₄	—	2	4	no	—
412	D₄	—	2	4	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	8	8	no	—
439	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
440	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
441	C₂×C₄	C₇×#135	1	2	yes	—
442	C₂×C₄	C₇×#135	1	2	yes	—
443	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
445	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
446	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
447	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	1	no	—
452	C₈	C₄×C₇×D₄	1	4	yes	—
453	C₇	#23186	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
462	C₂²	C₇×D₄²	1	1	yes	characteristic
463	C₂²	C₇×#550	1	1	yes	characteristic
464	C₂²	C₂×C₇×#135	1	1	yes	characteristic
465	C₂²	C₂×C₇×#135	1	1	yes	characteristic
466	C₂²	C₇×#576	1	1	yes	characteristic
467	C₂²	C₇×#578	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	4	no	—
476	C₄	—	8	2	no	—
477	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
478	C₄	C₇×#518	1	1	yes	characteristic
479	C₄	C₇×#550	1	1	yes	characteristic
480	C₄	C₇×#559	1	1	yes	characteristic
481	C₂	—	8	4	no	—
482	C₂	C₇×#2366	1	1	yes	characteristic
483	C₂	C₄×C₇×#135	1	1	yes	characteristic
484	C₂	C₇×#2951	1	1	yes	characteristic
485	C₂	C₇×#3280	1	1	yes	characteristic
486	C₂	C₇×#3285	1	1	yes	characteristic
487	C₂	C₇×#3393	1	1	yes	characteristic
488	C₂	C₇×#3396	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×C₄×C₇×Q₁₆	C₂	semidirect
4. C₇×#2367	C₂	semidirect
5. C₇×#1983	C₂	semidirect
7. C₇×#1969	C₂	semidirect
8. C₇×#1880	C₂	semidirect
9. C₇×#1877	C₂	semidirect
10. C₄×C₇×#107	C₂	semidirect
11. C₇×C₈×C₄⋊C₄	C₂	semidirect
18. C₇×#495	C₄	semidirect
42. #23186	C₇	direct (N × H)
48. C₂×C₇×Q₁₆	C₂×C₄	semidirect
51. C₂×C₇×SD₁₆	C₂×C₄	semidirect
60. C₇×#124	C₂×C₄	semidirect
89. C₄×C₇×C₈	C₂×C₄	semidirect
96. C₂×C₄×Q₁₆	C₂×C₇	semidirect
98. #2367	C₂×C₇	semidirect
99. #1983	C₂×C₇	semidirect
101. #1969	C₂×C₇	semidirect
102. #1880	C₂×C₇	semidirect
103. #1877	C₂×C₇	semidirect
104. C₄×#107	C₂×C₇	semidirect
105. C₈×C₄⋊C₄	C₂×C₇	semidirect
173. #495	C₄×C₇	semidirect
256. C₂×Q₁₆	C₂×C₄×C₇	semidirect
259. C₂×SD₁₆	C₂×C₄×C₇	semidirect
268. #124	C₂×C₄×C₇	semidirect
297. C₄×C₈	C₂×C₄×C₇	semidirect
453. C₇	#23186	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×C₄×C₇×Q₁₆	2
C₂×C₄×C₇×D₈	2
C₇×#2367	2
C₇×#1983	2
C₇×#1970	2
C₇×#1969	2
C₇×#1880	2
C₇×#1877	2
C₄×C₇×#107	2
C₇×C₈×C₄⋊C₄	2
#23186	7

Subgroups — C7×#23186 #13200402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23186 #13200402