Subgroups — #13325514

Order 1792.

650 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic
2	#11739968	C₂	1	1	yes	maximal, characteristic, complemented
3	#11739967	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729395	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729395	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728657	C₂	1	2	yes	maximal, complemented
7	#11728654	C₂	1	2	yes	maximal, complemented
8	SD₁₆⋊(C₇⋊C₈)	C₂	1	2	yes	maximal, complemented
9	#11728633	C₂	1	2	yes	maximal, complemented
10	#11727485	C₂	1	1	yes	maximal, characteristic, complemented
11	#11727479	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	C₄	1	1	yes	characteristic
13	C₄×C₇×#41	C₂²	1	1	yes	characteristic
14	C₄×C₇×#41	C₂²	1	1	yes	characteristic
15	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic
16	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₇×SD₁₆	C₄	1	1	yes	characteristic
18	C₄×C₇×SD₁₆	C₄	1	1	yes	characteristic
19	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₄×C₇×D₈	C₄	1	1	yes	characteristic
22	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
23	C₇×#427	C₄	1	1	yes	characteristic
24	C₇×#416	C₄	1	1	yes	characteristic
25	C₇×#416	C₄	1	1	yes	characteristic
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	#89796	C₂²	1	2	yes	—
28	Q₈×C₇⋊C₈	C₂²	1	2	yes	—
29	#89784	—	2	2	no	—
30	#89784	C₂²	1	2	yes	—
31	#89783	—	2	2	no	—
32	D₄×C₇⋊C₈	C₂²	1	2	yes	—
33	#89698	—	2	1	no	—
34	#89697	—	2	1	no	—
35	#89697	C₂²	1	1	yes	characteristic
36	#89696	—	2	1	no	—
37	#89696	C₂²	1	1	yes	characteristic
38	#89696	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊(C₇⋊C₈)	—	2	1	no	—
40	C₄×#1136	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₇⋊C₈)	C₂²	1	2	yes	—
42	Q₈⋊(C₇⋊C₈)	C₂²	1	2	yes	—
43	D₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
44	D₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
45	#89253	C₂²	1	2	yes	—
46	#89253	C₂²	1	2	yes	—
47	#89250	C₂²	1	2	yes	—
48	#89249	C₂²	1	2	yes	—
49	#18061	—	7	1	no	maximal, Sylow
50	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
51	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
52	C₇×#135	—	2	4	no	—
53	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
59	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
60	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
62	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
63	C₄×C₇×D₄	—	2	1	no	—
64	C₄×C₇×D₄	—	2	1	no	—
65	C₄×C₇×D₄	—	2	1	no	—
66	C₄×C₇×D₄	—	2	1	no	—
67	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
68	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
69	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
70	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
71	C₇×#117	—	2	1	no	—
72	C₇×#117	—	2	1	no	—
73	C₇×#117	C₂×C₄	1	1	yes	characteristic
74	C₇×#117	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₇	—	2	1	no	—
76	C₂×C₄²×C₇	—	2	1	no	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×#1136	—	2	1	no	—
79	C₂×#1136	—	2	1	no	—
80	C₂×#1136	—	2	1	no	—
81	C₂×#1136	—	2	2	no	—
82	C₂²×C₇⋊C₈	—	2	2	no	—
83	C₇×#107	C₂×C₄	1	1	yes	characteristic
84	C₇×#107	C₂×C₄	1	1	yes	characteristic
85	C₇×#106	C₂×C₄	1	1	yes	characteristic
86	C₇×#106	C₂×C₄	1	1	yes	characteristic
87	C₇×#103	C₂×C₄	1	1	yes	characteristic
88	C₇×#103	C₂×C₄	1	1	yes	characteristic
89	C₇×#103	C₂×C₄	1	1	yes	characteristic
90	C₇×#103	C₂×C₄	1	1	yes	characteristic
91	C₇×#102	C₂×C₄	1	1	yes	characteristic
92	C₇×#102	C₂×C₄	1	1	yes	characteristic
93	C₇×#102	C₂×C₄	1	1	yes	characteristic
94	C₇×#102	C₂×C₄	1	1	yes	characteristic
95	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
97	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
98	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
99	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
100	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
101	C₂²⋊(C₇⋊C₈)	D₄	1	2	yes	—
102	C₄⋊(C₇⋊C₈)	—	2	1	no	—
103	C₄⋊(C₇⋊C₈)	—	2	1	no	—
104	C₄⋊(C₇⋊C₈)	—	2	2	no	—
105	C₄⋊(C₇⋊C₈)	—	2	2	no	—
106	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
107	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
108	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
109	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
110	#6377	—	2	1	no	—
111	#6377	—	2	2	no	—
112	C₄×C₇⋊C₈	—	2	2	no	—
113	C₄×C₇⋊C₈	C₂³	1	2	yes	—
114	C₄×C₇⋊C₈	C₂³	1	2	yes	—
115	#2991	—	7	1	no	—
116	#2990	—	7	1	no	—
117	C₄×#135	D₇	1	1	yes	characteristic
118	#1592	—	7	2	no	—
119	#1584	—	7	2	no	—
120	#1581	—	7	2	no	—
121	SD₁₆⋊C₈	—	7	2	no	—
122	#1567	—	7	1	no	—
123	#1489	—	7	1	no	—
124	#1489	—	7	1	no	—
125	#1451	—	7	1	no	—
126	C₇×#41	—	2	2	no	—
127	C₇×#41	—	2	2	no	—
128	C₇×#41	—	4	1	no	—
129	C₇×#41	—	4	1	no	—
130	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₇×D₄	—	2	1	no	—
133	C₂×C₇×D₄	—	2	1	no	—
134	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	—	2	1	no	—
137	C₂²×C₄×C₇	—	2	1	no	—
138	C₂²×C₄×C₇	—	2	1	no	—
139	C₂²×C₄×C₇	—	2	1	no	—
140	C₂²×C₄×C₇	—	2	1	no	—
141	C₂²×C₄×C₇	—	2	1	no	—
142	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	#41	1	1	yes	characteristic
145	C₇×Q₁₆	—	2	2	no	—
146	C₇×SD₁₆	—	2	2	no	—
147	C₇×SD₁₆	M₁₆	1	4	yes	complemented
148	C₇×D₈	—	2	2	no	—
149	C₂×C₇×C₈	—	2	2	no	—
150	C₂×C₇×C₈	—	4	1	no	—
151	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
160	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
161	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
162	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
163	C₇×C₂²⋊C₄	—	2	1	no	—
164	C₇×C₂²⋊C₄	—	2	1	no	—
165	C₇×C₂²⋊C₄	—	2	1	no	—
166	C₇×C₂²⋊C₄	—	2	1	no	—
167	C₇×C₂²⋊C₄	—	2	1	no	—
168	C₇×C₂²⋊C₄	—	2	1	no	—
169	C₄²×C₇	—	2	1	no	—
170	C₄²×C₇	—	2	1	no	—
171	C₄²×C₇	—	2	1	no	—
172	C₄²×C₇	—	2	1	no	—
173	C₄²×C₇	—	2	1	no	—
174	C₄²×C₇	—	2	1	no	—
175	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₇	#41	1	1	yes	characteristic
178	C₄²×C₇	C₂⁴	1	1	yes	characteristic
179	#1136	—	4	2	no	—
180	#1136	—	8	2	no	—
181	#1136	—	8	1	no	—
182	#1136	—	8	1	no	—
183	C₂×C₇⋊C₈	—	2	2	no	—
184	C₂×C₇⋊C₈	—	2	2	no	—
185	C₂×C₇⋊C₈	—	2	2	no	—
186	C₂×C₇⋊C₈	—	8	2	no	—
187	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
188	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
189	C₂×#135	Dic₇	1	1	yes	characteristic
190	C₄×#41	C₂×D₇	1	1	yes	characteristic
191	C₄×#41	C₂×D₇	1	1	yes	characteristic
192	#446	—	7	2	no	—
193	C₈×Q₈	—	7	2	no	—
194	C₄×Q₁₆	Dic₇	1	1	yes	characteristic
195	C₄×Q₁₆	C₂×D₇	1	1	yes	characteristic
196	C₄×SD₁₆	Dic₇	1	1	yes	characteristic
197	C₄×SD₁₆	Dic₇	1	1	yes	characteristic
198	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
199	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
200	C₄×D₈	Dic₇	1	1	yes	characteristic
201	C₄×D₈	C₂×D₇	1	1	yes	characteristic
202	#436	—	7	2	no	—
203	#436	—	14	2	no	—
204	#435	—	14	2	no	—
205	C₈×D₄	—	7	2	no	—
206	#432	—	14	1	no	—
207	#431	—	7	1	no	—
208	#431	—	14	1	no	—
209	#427	Dic₇	1	1	yes	characteristic
210	#423	—	7	1	no	—
211	#423	—	7	1	no	—
212	#423	—	14	1	no	—
213	C₂×C₄⋊C₈	—	14	1	no	—
214	#416	Dic₇	1	1	yes	characteristic
215	#416	Dic₇	1	1	yes	characteristic
216	C₄×M₁₆	—	7	1	no	—
217	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
218	#335	—	7	2	no	—
219	#335	—	7	2	no	—
220	Q₈⋊C₈	—	7	2	no	—
221	Q₈⋊C₈	—	7	2	no	—
222	D₄⋊C₈	—	7	2	no	—
223	D₄⋊C₈	—	7	2	no	—
224	#322	—	7	2	no	—
225	#322	—	7	2	no	—
226	C₂³×C₇	—	2	1	no	—
227	C₂³×C₇	—	2	1	no	—
228	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
229	C₇×Q₈	—	2	1	no	—
230	C₇×Q₈	—	2	1	no	—
231	C₇×Q₈	—	2	1	no	—
232	C₇×Q₈	C₂×M₁₆	1	2	yes	—
233	C₇×D₄	—	2	1	no	—
234	C₇×D₄	—	2	1	no	—
235	C₇×D₄	—	2	1	no	—
236	C₇×D₄	—	4	2	no	—
237	C₇×D₄	—	4	2	no	—
238	C₇×D₄	C₂×M₁₆	1	2	yes	—
239	C₂×C₄×C₇	—	2	1	no	—
240	C₂×C₄×C₇	—	2	1	no	—
241	C₂×C₄×C₇	—	2	1	no	—
242	C₂×C₄×C₇	—	2	1	no	—
243	C₂×C₄×C₇	—	2	1	no	—
244	C₂×C₄×C₇	—	2	2	no	—
245	C₂×C₄×C₇	—	2	1	no	—
246	C₂×C₄×C₇	—	2	1	no	—
247	C₂×C₄×C₇	—	2	1	no	—
248	C₂×C₄×C₇	—	2	1	no	—
249	C₂×C₄×C₇	—	2	1	no	—
250	C₂×C₄×C₇	—	4	2	no	—
251	C₂×C₄×C₇	—	4	2	no	—
252	C₂×C₄×C₇	—	4	1	no	—
253	C₂×C₄×C₇	—	4	1	no	—
254	C₂×C₄×C₇	—	4	1	no	—
255	C₂×C₄×C₇	—	4	1	no	—
256	C₂×C₄×C₇	—	4	2	no	—
257	C₂×C₄×C₇	—	4	2	no	—
258	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
264	C₇×C₈	—	2	1	no	—
265	C₇×C₈	—	2	1	no	—
266	C₇×C₈	—	2	1	no	—
267	C₇×C₈	C₂×M₁₆	1	2	yes	—
268	C₇⋊C₈	—	2	2	no	—
269	C₇⋊C₈	—	2	2	no	—
270	C₇⋊C₈	—	4	2	no	—
271	C₇⋊C₈	—	4	2	no	—
272	C₇⋊C₈	—	4	2	no	—
273	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
274	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
275	#135	—	2	4	no	—
276	C₂×Q₁₆	C₂×Dic₇	1	1	yes	characteristic
277	C₂×SD₁₆	C₂×Dic₇	1	1	yes	characteristic
278	C₂×SD₁₆	C₂×Dic₇	1	1	yes	characteristic
279	C₂×D₈	C₂×Dic₇	1	1	yes	characteristic
280	C₂×M₁₆	—	14	2	no	—
281	C₂×M₁₆	—	14	1	no	—
282	C₂×M₁₆	—	14	1	no	—
283	C₂×M₁₆	—	14	1	no	—
284	C₂²×C₈	—	14	2	no	—
285	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
286	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
287	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
288	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
290	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
296	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
298	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	C₂×Dic₇	1	1	yes	characteristic
302	#117	C₂×Dic₇	1	1	yes	characteristic
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
306	#107	C₂×Dic₇	1	1	yes	characteristic
307	#107	C₂×Dic₇	1	1	yes	characteristic
308	#106	C₂×Dic₇	1	1	yes	characteristic
309	#106	C₂×Dic₇	1	1	yes	characteristic
310	C₄⋊C₈	—	7	1	no	—
311	C₄⋊C₈	—	7	1	no	—
312	C₄⋊C₈	—	7	2	no	—
313	C₄⋊C₈	—	7	2	no	—
314	C₄⋊C₈	—	14	2	no	—
315	C₄⋊C₈	—	14	2	no	—
316	C₄⋊C₈	—	14	1	no	—
317	C₄⋊C₈	—	14	1	no	—
318	#103	C₂×Dic₇	1	1	yes	characteristic
319	#103	C₂×Dic₇	1	1	yes	characteristic
320	#103	C₂×Dic₇	1	1	yes	characteristic
321	#103	C₂×Dic₇	1	1	yes	characteristic
322	#102	C₂×Dic₇	1	1	yes	characteristic
323	#102	C₂×Dic₇	1	1	yes	characteristic
324	#102	C₂×Dic₇	1	1	yes	characteristic
325	#102	C₂×Dic₇	1	1	yes	characteristic
326	C₂²⋊C₈	—	7	2	no	—
327	C₂²⋊C₈	—	14	2	no	—
328	C₂²⋊C₈	—	14	2	no	—
329	#97	—	14	2	no	—
330	#97	—	14	1	no	—
331	C₄×C₈	—	7	2	no	—
332	C₄×C₈	—	7	2	no	—
333	C₄×C₈	—	14	2	no	—
334	C₄×C₈	C₂×Dic₇	1	1	yes	characteristic
335	C₄×C₈	C₂×Dic₇	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
338	C₂²×C₇	—	2	1	no	—
339	C₂²×C₇	—	2	2	no	—
340	C₂²×C₇	—	2	1	no	—
341	C₂²×C₇	—	2	1	no	—
342	C₂²×C₇	—	4	1	no	—
343	C₂²×C₇	—	4	1	no	—
344	C₂²×C₇	—	4	1	no	—
345	C₂²×C₇	—	4	1	no	—
346	C₂²×C₇	—	4	1	no	—
347	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
348	C₄×C₇	—	2	1	no	—
349	C₄×C₇	—	2	2	no	—
350	C₄×C₇	—	2	1	no	—
351	C₄×C₇	—	2	1	no	—
352	C₄×C₇	—	4	1	no	—
353	C₄×C₇	—	4	1	no	—
354	C₄×C₇	—	4	1	no	—
355	C₄×C₇	—	4	1	no	—
356	C₄×C₇	—	4	1	no	—
357	C₄×C₇	#444	1	2	yes	—
358	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
359	C₄×C₇	#568	1	1	yes	characteristic
360	C₄×C₇	#576	1	1	yes	characteristic
361	C₄×C₇	#578	1	1	yes	characteristic
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	4	1	no	—
365	#41	—	4	1	no	—
366	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
367	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
371	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
379	C₂²×C₄	#1159	1	1	yes	characteristic
380	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
381	Q₁₆	—	2	2	no	—
382	SD₁₆	—	2	2	no	—
383	SD₁₆	#1136	1	4	yes	complemented
384	D₈	—	2	2	no	—
385	M₁₆	—	28	2	no	—
386	M₁₆	—	56	2	no	—
387	M₁₆	—	56	1	no	—
388	M₁₆	—	56	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	1	no	—
391	C₂×C₈	—	7	2	no	—
392	C₂×C₈	—	7	2	no	—
393	C₂×C₈	—	14	2	no	—
394	C₂×C₈	—	14	2	no	—
395	C₂×C₈	—	14	2	no	—
396	C₂×C₈	—	56	2	no	—
397	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
398	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
399	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
400	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
406	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
407	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
408	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	D₄×D₇	1	1	yes	characteristic
422	C₄²	#1159	1	1	yes	characteristic
423	C₄²	C₂²×Dic₇	1	1	yes	characteristic
424	C₄²	C₂³×D₇	1	1	yes	characteristic
425	C₂×C₇	—	4	1	no	—
426	C₂×C₇	—	4	2	no	—
427	C₂×C₇	—	8	1	no	—
428	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
429	C₂×C₇	#2951	1	1	yes	characteristic
430	C₂×C₇	C₂×#444	1	1	yes	characteristic
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	D₄×Dic₇	1	1	yes	characteristic
434	Q₈	—	2	1	no	—
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	C₂×#1136	1	2	yes	—
438	D₄	—	2	1	no	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	C₂×#1136	1	2	yes	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
464	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
465	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#1159	1	1	yes	characteristic
468	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
469	C₈	—	2	1	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	14	2	no	—
473	C₈	—	14	2	no	—
474	C₈	—	28	2	no	—
475	C₈	—	28	2	no	—
476	C₈	—	28	2	no	—
477	C₈	C₂×#1136	1	2	yes	—
478	C₇	#18061	1	1	yes	characteristic, complemented, Sylow
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	#89969	1	2	yes	—
499	C₄	#90460	1	1	yes	characteristic
500	C₄	#90462	1	1	yes	characteristic
501	C₄	C₂²×#1136	1	1	yes	characteristic
502	C₄	#90510	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	1	no	—
506	C₂	D₄×#1136	1	1	yes	characteristic
507	C₂	#11741343	1	1	yes	characteristic
508	C₂	C₂×#89969	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₄×C₇×#135	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×C₇×#135	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	C₄×#135	D₇
hypocenter	C₇	#18061
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
2. #11739968	C₂	semidirect
3. #11739967	C₂	semidirect
4. #11729395	C₂	semidirect
5. #11729395	C₂	semidirect
6. #11728657	C₂	semidirect
7. #11728654	C₂	semidirect
8. SD₁₆⋊(C₇⋊C₈)	C₂	semidirect
9. #11728633	C₂	semidirect
10. #11727485	C₂	semidirect
11. #11727479	C₂	semidirect
147. C₇×SD₁₆	M₁₆	semidirect
383. SD₁₆	#1136	semidirect
478. C₇	#18061	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₇×#135	2
#11739968	2
#11739967	2
#11729395	2
#11728657	2
#11728654	2
SD₁₆⋊(C₇⋊C₈)	2
#11728633	2
#11727485	2
#11727479	2
#18061	7