Subgroups — C₇×#23182 #13200398

Order 1792.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₇×#2366	C₂	1	1	yes	maximal, characteristic
4	C₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1982	C₂	1	1	yes	maximal, characteristic
6	C₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1968	C₂	1	2	yes	maximal, complemented
8	C₇×#1880	C₂	1	2	yes	maximal, complemented
9	C₇×#1877	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#127	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
17	C₂×C₄×C₇×D₄	—	2	1	no	—
18	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
19	C₇×#492	C₄	1	8	yes	complemented
20	C₄×C₇×SD₁₆	—	2	8	no	—
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	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	2	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#391	C₂²	1	2	yes	—
31	C₇×#390	—	2	1	no	—
32	C₇×#390	C₂²	1	2	yes	—
33	C₇×#389	—	2	1	no	—
34	C₇×#387	—	2	2	no	—
35	C₇×#386	—	2	2	no	—
36	C₄×C₇×C₄⋊C₄	—	2	1	no	—
37	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₇×#340	C₂²	1	1	yes	characteristic
41	C₇×#340	C₂²	1	1	yes	characteristic
42	C₇×#336	C₂²	1	2	yes	—
43	#23182	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	C₂³	1	2	yes	—
45	C₂²×C₇×D₄	—	2	1	no	—
46	C₂²×C₇×D₄	—	2	1	no	—
47	C₂²×C₇×D₄	C₂³	1	2	yes	—
48	C₂³×C₄×C₇	—	2	2	no	—
49	C₂×C₇×SD₁₆	—	2	4	no	—
50	C₂×C₇×SD₁₆	—	2	4	no	—
51	C₂×C₇×SD₁₆	—	4	2	no	—
52	C₂×C₇×SD₁₆	—	4	2	no	—
53	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	complemented
54	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	complemented
55	C₂²×C₇×C₈	C₂³	1	2	yes	—
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₇×C₄⋊Q₈	—	2	2	no	—
59	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
60	C₇×#127	—	2	2	no	—
61	C₇×#127	C₂×C₄	1	4	yes	—
62	C₄×C₇×Q₈	—	2	4	no	—
63	C₄×C₇×Q₈	—	4	2	no	—
64	C₄×C₇×D₄	—	2	4	no	—
65	C₄×C₇×D₄	—	4	2	no	—
66	C₄×C₇×D₄	—	4	4	no	—
67	C₂×C₇×C₄⋊C₄	—	2	1	no	—
68	C₂×C₇×C₄⋊C₄	—	2	1	no	—
69	C₂×C₇×C₄⋊C₄	—	2	2	no	—
70	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₄²×C₇	—	2	1	no	—
80	C₂×C₄²×C₇	—	2	2	no	—
81	C₂×C₄²×C₇	—	2	1	no	—
82	C₂×C₄²×C₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
84	C₇×#106	—	2	2	no	—
85	C₇×#106	D₄	1	4	yes	complemented
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×#103	—	2	4	no	—
88	C₇×#103	—	4	2	no	—
89	C₇×#102	—	2	4	no	—
90	C₇×#102	—	4	2	no	—
91	C₄×C₇×C₈	—	2	4	no	—
92	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
93	C₇×#95	—	2	2	no	—
94	C₇×#95	—	2	1	no	—
95	C₇×#95	—	2	1	no	—
96	C₇×#95	—	2	2	no	—
97	C₇×#95	D₄	1	2	yes	—
98	C₂×#492	C₂×C₇	1	1	yes	characteristic
99	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	complemented
100	#2366	C₂×C₇	1	1	yes	characteristic
101	#2365	C₂×C₇	1	1	yes	characteristic, complemented
102	#1982	C₂×C₇	1	1	yes	characteristic
103	#1981	C₂×C₇	1	1	yes	characteristic, complemented
104	#1968	C₂×C₇	1	2	yes	complemented
105	#1880	C₂×C₇	1	2	yes	complemented
106	#1877	C₂×C₇	1	2	yes	complemented
107	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
108	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
109	C₂⁴×C₇	—	2	2	no	—
110	C₂×C₇×Q₈	—	2	2	no	—
111	C₂×C₇×Q₈	—	2	2	no	—
112	C₂×C₇×Q₈	—	2	2	no	—
113	C₂×C₇×Q₈	—	2	2	no	—
114	C₂×C₇×Q₈	—	2	2	no	—
115	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
116	C₂×C₇×D₄	—	2	4	no	—
117	C₂×C₇×D₄	—	2	4	no	—
118	C₂×C₇×D₄	—	2	2	no	—
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	—	2	2	no	—
122	C₂×C₇×D₄	—	2	2	no	—
123	C₂×C₇×D₄	—	4	2	no	—
124	C₂×C₇×D₄	—	4	2	no	—
125	C₂×C₇×D₄	—	8	1	no	—
126	C₂×C₇×D₄	—	8	1	no	—
127	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	1	no	—
133	C₂²×C₄×C₇	—	4	4	no	—
134	C₂²×C₄×C₇	—	4	4	no	—
135	C₂²×C₄×C₇	—	8	2	no	—
136	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
141	C₇×SD₁₆	—	2	16	no	—
142	C₇×SD₁₆	—	4	8	no	—
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₇×C₈	#41	1	2	yes	—
152	C₇×C₄⋊C₄	—	2	4	no	—
153	C₇×C₄⋊C₄	—	2	4	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	2	1	no	—
158	C₇×C₄⋊C₄	—	2	1	no	—
159	C₇×C₄⋊C₄	—	2	1	no	—
160	C₇×C₄⋊C₄	—	2	1	no	—
161	C₇×C₄⋊C₄	—	4	4	no	—
162	C₇×C₄⋊C₄	SD₁₆	1	4	yes	complemented
163	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₇×C₂²⋊C₄	—	4	4	no	—
166	C₇×C₂²⋊C₄	—	4	4	no	—
167	C₇×C₂²⋊C₄	—	8	2	no	—
168	C₄²×C₇	—	2	2	no	—
169	C₄²×C₇	—	2	2	no	—
170	C₄²×C₇	—	4	4	no	—
171	C₄²×C₇	—	4	2	no	—
172	C₄²×C₇	—	4	2	no	—
173	C₄²×C₇	C₂²×C₄	1	2	yes	—
174	C₄²×C₇	#41	1	2	yes	—
175	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
176	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
177	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
178	C₂×#127	C₂²×C₇	1	1	yes	characteristic
179	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
180	C₂×C₄×D₄	—	2	1	no	—
181	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
182	#492	C₄×C₇	1	8	yes	complemented
183	C₄×SD₁₆	—	2	8	no	—
184	C₂×#106	C₂²×C₇	1	1	yes	characteristic
185	C₂×#106	C₂²×C₇	1	1	yes	characteristic
186	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
187	C₂×#103	C₂²×C₇	1	2	yes	—
188	C₂×#103	C₂²×C₇	1	2	yes	—
189	C₂×#102	C₂²×C₇	1	2	yes	—
190	C₂×#102	C₂²×C₇	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
193	#391	C₂²×C₇	1	2	yes	—
194	#390	—	2	1	no	—
195	#390	C₂²×C₇	1	2	yes	—
196	#389	—	2	1	no	—
197	#387	—	2	2	no	—
198	#386	—	2	2	no	—
199	C₄×C₄⋊C₄	—	2	1	no	—
200	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
201	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
202	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
203	#340	C₂²×C₇	1	1	yes	characteristic
204	#340	C₂²×C₇	1	1	yes	characteristic
205	#336	C₂²×C₇	1	2	yes	—
206	C₂³×C₇	—	2	4	no	—
207	C₂³×C₇	—	4	2	no	—
208	C₂³×C₇	—	4	2	no	—
209	C₂³×C₇	—	4	2	no	—
210	C₂³×C₇	—	4	2	no	—
211	C₂³×C₇	—	4	2	no	—
212	C₂³×C₇	—	4	2	no	—
213	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
214	C₇×Q₈	—	2	4	no	—
215	C₇×Q₈	—	2	4	no	—
216	C₇×Q₈	—	4	2	no	—
217	C₇×Q₈	—	4	2	no	—
218	C₇×D₄	—	2	4	no	—
219	C₇×D₄	—	2	4	no	—
220	C₇×D₄	—	4	2	no	—
221	C₇×D₄	—	4	2	no	—
222	C₇×D₄	—	4	8	no	—
223	C₇×D₄	—	8	4	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	4	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	4	1	no	—
237	C₂×C₄×C₇	—	4	1	no	—
238	C₂×C₄×C₇	—	4	1	no	—
239	C₂×C₄×C₇	—	4	1	no	—
240	C₂×C₄×C₇	—	4	1	no	—
241	C₂×C₄×C₇	—	4	1	no	—
242	C₂×C₄×C₇	—	4	1	no	—
243	C₂×C₄×C₇	—	4	1	no	—
244	C₂×C₄×C₇	—	4	1	no	—
245	C₂×C₄×C₇	—	4	1	no	—
246	C₂×C₄×C₇	—	8	8	no	—
247	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
249	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
250	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
251	C₂×C₄×C₇	#135	1	2	yes	—
252	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
258	C₇×C₈	—	2	2	no	—
259	C₇×C₈	—	4	2	no	—
260	C₇×C₈	C₄×D₄	1	4	yes	complemented
261	C₂²×Q₈	C₂³×C₇	1	2	yes	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	C₂³×C₇	1	2	yes	—
265	C₂³×C₄	—	2	2	no	—
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×SD₁₆	—	2	4	no	—
268	C₂×SD₁₆	—	4	2	no	—
269	C₂×SD₁₆	—	4	2	no	—
270	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
271	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
272	C₂²×C₈	C₂³×C₇	1	2	yes	—
273	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
277	#127	—	2	2	no	—
278	#127	C₂×C₄×C₇	1	4	yes	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	4	2	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	4	2	no	—
283	C₄×D₄	—	4	4	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₇	1	2	yes	—
300	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
301	#106	—	2	2	no	—
302	#106	C₇×D₄	1	4	yes	complemented
303	C₄⋊C₈	—	2	2	no	—
304	#103	—	2	4	no	—
305	#103	—	4	2	no	—
306	#102	—	2	4	no	—
307	#102	—	4	2	no	—
308	C₄×C₈	—	2	4	no	—
309	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
310	#95	—	2	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	C₇×D₄	1	2	yes	—
315	C₂²×C₇	—	4	4	no	—
316	C₂²×C₇	—	4	4	no	—
317	C₂²×C₇	—	4	4	no	—
318	C₂²×C₇	—	8	2	no	—
319	C₂²×C₇	—	8	2	no	—
320	C₂²×C₇	—	8	2	no	—
321	C₂²×C₇	—	8	2	no	—
322	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
323	C₂²×C₇	D₄²	1	1	yes	characteristic
324	C₂²×C₇	#550	1	1	yes	characteristic
325	C₂²×C₇	C₂²×SD₁₆	1	1	yes	characteristic
326	C₂²×C₇	C₂×#135	1	1	yes	characteristic
327	C₂²×C₇	#577	1	1	yes	characteristic
328	C₂²×C₇	#577	1	1	yes	characteristic
329	C₄×C₇	—	2	2	no	—
330	C₄×C₇	—	2	4	no	—
331	C₄×C₇	—	4	4	no	—
332	C₄×C₇	—	4	2	no	—
333	C₄×C₇	—	4	2	no	—
334	C₄×C₇	—	4	2	no	—
335	C₄×C₇	—	8	1	no	—
336	C₄×C₇	—	8	1	no	—
337	C₄×C₇	C₄×SD₁₆	1	4	yes	complemented
338	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
339	C₄×C₇	#518	1	1	yes	characteristic
340	C₄×C₇	#550	1	1	yes	characteristic
341	C₄×C₇	#559	1	1	yes	characteristic
342	C₂⁴	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	8	1	no	—
359	C₂×D₄	—	8	1	no	—
360	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	—	8	2	no	—
369	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
370	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
372	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
374	SD₁₆	—	2	16	no	—
375	SD₁₆	—	4	8	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
382	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
383	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
384	C₂×C₈	C₇×#41	1	2	yes	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	C₇×SD₁₆	1	4	yes	complemented
396	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	8	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	4	4	no	—
404	C₄²	—	4	2	no	—
405	C₄²	—	4	2	no	—
406	C₄²	C₂²×C₄×C₇	1	2	yes	—
407	C₄²	C₇×#41	1	2	yes	—
408	C₂×C₇	—	8	4	no	—
409	C₂×C₇	#2366	1	1	yes	characteristic
410	C₂×C₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
411	C₂×C₇	#2949	1	1	yes	characteristic
412	C₂×C₇	D₄×SD₁₆	1	1	yes	characteristic
413	C₂×C₇	#3284	1	1	yes	characteristic
414	C₂×C₇	#3392	1	1	yes	characteristic
415	C₂×C₇	#3394	1	1	yes	characteristic
416	C₂³	—	2	4	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
424	Q₈	—	2	4	no	—
425	Q₈	—	2	4	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	8	no	—
433	D₄	—	8	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	8	8	no	—
457	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
458	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
459	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
460	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
461	C₂×C₄	C₇×#135	1	2	yes	—
462	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
464	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
465	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
466	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	4	2	no	—
470	C₈	C₄×C₇×D₄	1	4	yes	complemented
471	C₇	#23182	1	1	yes	characteristic, direct product factor, Sylow
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
480	C₂²	C₇×D₄²	1	1	yes	characteristic
481	C₂²	C₇×#550	1	1	yes	characteristic
482	C₂²	C₂²×C₇×SD₁₆	1	1	yes	characteristic
483	C₂²	C₂×C₇×#135	1	1	yes	characteristic
484	C₂²	C₇×#577	1	1	yes	characteristic
485	C₂²	C₇×#577	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	4	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	8	1	no	—
493	C₄	—	8	1	no	—
494	C₄	C₄×C₇×SD₁₆	1	4	yes	complemented
495	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
496	C₄	C₇×#518	1	1	yes	characteristic
497	C₄	C₇×#550	1	1	yes	characteristic
498	C₄	C₇×#559	1	1	yes	characteristic
499	C₂	—	8	4	no	—
500	C₂	C₇×#2366	1	1	yes	characteristic
501	C₂	C₂×C₄×C₇×SD₁₆	1	1	yes	characteristic
502	C₂	C₇×#2949	1	1	yes	characteristic
503	C₂	C₇×D₄×SD₁₆	1	1	yes	characteristic
504	C₂	C₇×#3284	1	1	yes	characteristic
505	C₂	C₇×#3392	1	1	yes	characteristic
506	C₂	C₇×#3394	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	C₂×C₇×#127	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×SD₁₆	C₂	semidirect
4. C₇×#2365	C₂	semidirect
6. C₇×#1981	C₂	semidirect
7. C₇×#1968	C₂	semidirect
8. C₇×#1880	C₂	semidirect
9. C₇×#1877	C₂	semidirect
10. C₄×C₇×#106	C₂	semidirect
11. C₇×C₈×C₄⋊C₄	C₂	semidirect
19. C₇×#492	C₄	semidirect
43. #23182	C₇	direct (N × H)
53. C₂×C₇×SD₁₆	C₂×C₄	semidirect
54. C₂×C₇×SD₁₆	C₂×C₄	semidirect
59. C₇×C₄⋊Q₈	C₂×C₄	semidirect
85. C₇×#106	D₄	semidirect
92. C₄×C₇×C₈	C₂×C₄	semidirect
99. C₂×C₄×SD₁₆	C₂×C₇	semidirect
101. #2365	C₂×C₇	semidirect
103. #1981	C₂×C₇	semidirect
104. #1968	C₂×C₇	semidirect
105. #1880	C₂×C₇	semidirect
106. #1877	C₂×C₇	semidirect
107. C₄×#106	C₂×C₇	semidirect
108. C₈×C₄⋊C₄	C₂×C₇	semidirect
162. C₇×C₄⋊C₄	SD₁₆	semidirect
182. #492	C₄×C₇	semidirect
260. C₇×C₈	C₄×D₄	semidirect
270. C₂×SD₁₆	C₂×C₄×C₇	semidirect
271. C₂×SD₁₆	C₂×C₄×C₇	semidirect
276. C₄⋊Q₈	C₂×C₄×C₇	semidirect
302. #106	C₇×D₄	semidirect
309. C₄×C₈	C₂×C₄×C₇	semidirect
337. C₄×C₇	C₄×SD₁₆	semidirect
395. C₄⋊C₄	C₇×SD₁₆	semidirect
470. C₈	C₄×C₇×D₄	semidirect
471. C₇	#23182	direct (N × H)
494. C₄	C₄×C₇×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#492	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2366	2
C₇×#2365	2
C₇×#1982	2
C₇×#1981	2
C₇×#1968	2
C₇×#1880	2
C₇×#1877	2
C₄×C₇×#106	2
C₇×C₈×C₄⋊C₄	2
#23182	7

Subgroups — C7×#23182 #13200398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23182 #13200398