Subgroups — #13507327

Order 1792.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11736001	C₂	1	1	yes	maximal, characteristic
2	C₇×#2108	C₂	1	1	yes	maximal, characteristic, complemented
3	#11729187	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729184	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₆×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727637	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726829	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726828	C₂	1	1	yes	maximal, characteristic, complemented
10	#11726827	C₂	1	1	yes	maximal, characteristic, complemented
11	#11726822	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₆×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#11726805	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₆×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
16	#90219	C₄	1	1	yes	characteristic
17	C₂×C₇×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₇×C₁₆	C₂²	1	1	yes	characteristic
19	C₇×#405	C₂²	1	1	yes	characteristic
20	#89900	C₄	1	1	yes	characteristic
21	#89899	C₄	1	1	yes	characteristic
22	C₈×C₂²⋊D₇	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₇	C₂²	1	1	yes	characteristic
24	#89772	C₄	1	1	yes	characteristic
25	C₂×#6372	C₂²	1	1	yes	characteristic
26	C₂×D₇×C₁₆	C₂²	1	1	yes	characteristic
27	C₂×D₇×C₁₆	C₂²	1	1	yes	characteristic
28	C₂×D₇×C₁₆	C₂²	1	1	yes	characteristic
29	#89481	C₄	1	1	yes	characteristic
30	#89478	C₄	1	1	yes	characteristic
31	#89477	C₄	1	1	yes	characteristic
32	#89473	C₄	1	1	yes	characteristic
33	#89461	C₂²	1	1	yes	characteristic
34	C₈×D₂₈	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
36	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
37	C₇×#346	C₂²	1	1	yes	characteristic
38	C₇×#346	C₂²	1	1	yes	characteristic
39	C₄×C₇×C₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₇×C₁₆	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
42	C₂²⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
43	(C₂×D₇)⋊C₁₆	C₂²	1	1	yes	characteristic
44	(C₂×D₇)⋊C₁₆	C₂²	1	1	yes	characteristic
45	(C₂×D₇)⋊C₁₆	C₂²	1	1	yes	characteristic
46	(C₂×D₇)⋊C₁₆	C₂²	1	1	yes	characteristic
47	#89297	C₂²	1	1	yes	characteristic
48	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
49	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
50	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
51	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
52	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
53	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
54	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
55	C₄⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
56	C₄⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
57	#89256	C₂²	1	1	yes	characteristic
58	C₄×C₇⋊C₁₆	C₂²	1	1	yes	characteristic
59	#33480	—	7	1	no	maximal, Sylow
60	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
62	C₇×#117	C₂×C₄	1	1	yes	characteristic
63	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
65	C₂×#1131	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
69	#6461	C₈	1	1	yes	characteristic
70	#6459	C₈	1	1	yes	characteristic
71	#6457	C₈	1	1	yes	characteristic
72	#6452	C₈	1	1	yes	characteristic
73	#6448	C₈	1	1	yes	characteristic
74	#6447	C₈	1	1	yes	characteristic
75	#6446	C₈	1	1	yes	characteristic
76	#6442	C₈	1	1	yes	characteristic
77	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
78	#6435	C₂×C₄	1	1	yes	characteristic
79	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
81	C₇×M₃₂	—	2	2	no	—
82	C₂×C₇×C₁₆	—	2	2	no	—
83	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
87	C₇×#97	C₂×C₄	1	1	yes	characteristic
88	C₇×#97	C₂×C₄	1	1	yes	characteristic
89	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
97	#6389	C₂×C₄	1	1	yes	characteristic
98	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
99	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
100	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
101	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₇	C₂³	1	1	yes	characteristic
104	C₈×Dic₇	C₂³	1	1	yes	characteristic
105	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
109	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
110	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
111	#6377	C₂×C₄	1	1	yes	characteristic
112	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
113	#6372	—	2	2	no	—
114	D₇×C₁₆	—	2	2	no	—
115	D₇×C₁₆	—	2	2	no	—
116	D₇×C₁₆	—	2	2	no	—
117	#2966	—	7	1	no	—
118	#2183	—	7	1	no	—
119	Q₈×C₁₆	—	7	1	no	—
120	#2169	—	7	1	no	—
121	#2168	—	7	1	no	—
122	#2168	—	7	1	no	—
123	D₄×C₁₆	—	7	1	no	—
124	D₄×C₁₆	—	7	1	no	—
125	D₄×C₁₆	—	7	1	no	—
126	#2164	—	7	1	no	—
127	#2164	—	7	1	no	—
128	#2163	—	7	1	no	—
129	#2108	—	7	1	no	—
130	#2108	D₇	1	1	yes	characteristic, complemented
131	C₂×C₄×C₁₆	—	7	1	no	—
132	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊D₇	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₇	C₂×C₈	1	1	yes	characteristic
135	C₂×D₂₈	C₂×C₈	1	1	yes	characteristic
136	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
137	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
138	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×Dic₁₄	C₂×C₈	1	1	yes	characteristic
141	C₇×M₁₆	—	2	2	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
148	C₇×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
149	C₇×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
150	C₇×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
151	C₇×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
152	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²⋊Dic₇	C₂×C₈	1	1	yes	characteristic
155	C₂²⋊Dic₇	C₂×C₈	1	1	yes	characteristic
156	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
157	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
158	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
159	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
160	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
161	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
162	C₄⋊Dic₇	C₂×C₈	1	1	yes	characteristic
163	C₄⋊Dic₇	C₂×C₈	1	1	yes	characteristic
164	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
165	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
166	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
167	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
168	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
169	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
170	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
171	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
172	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
173	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
178	#1131	—	2	2	no	—
179	C₈×D₇	—	2	2	no	—
180	C₈×D₇	—	2	1	no	—
181	C₈×D₇	—	2	1	no	—
182	C₈×D₇	—	2	1	no	—
183	C₈×D₇	—	2	1	no	—
184	C₇×C₁₆	—	2	1	no	—
185	C₇×C₁₆	—	2	1	no	—
186	C₇×C₁₆	#41	1	2	yes	—
187	C₇×C₁₆	#41	1	2	yes	—
188	C₇⋊C₁₆	—	2	1	no	—
189	C₇⋊C₁₆	—	2	1	no	—
190	C₇⋊C₁₆	—	2	1	no	—
191	C₇⋊C₁₆	—	2	1	no	—
192	#529	—	7	1	no	—
193	C₂×M₃₂	—	7	1	no	—
194	C₂×M₃₂	C₂×D₇	1	1	yes	characteristic
195	C₂²×C₁₆	—	7	1	no	—
196	C₂²×C₁₆	—	7	1	no	—
197	C₂²×C₁₆	—	7	1	no	—
198	C₂²×C₁₆	C₂×D₇	1	1	yes	characteristic
199	#446	—	7	1	no	—
200	C₈×Q₈	—	7	1	no	—
201	#436	—	7	1	no	—
202	#435	—	7	1	no	—
203	#435	—	7	1	no	—
204	C₈×D₄	—	7	1	no	—
205	C₈×D₄	—	7	1	no	—
206	C₈×D₄	—	7	1	no	—
207	#433	—	7	1	no	—
208	#433	—	7	1	no	—
209	#432	—	7	1	no	—
210	#405	—	7	1	no	—
211	#405	C₂×D₇	1	1	yes	characteristic
212	C₂×C₄×C₈	—	7	1	no	—
213	C₄⋊C₁₆	—	7	1	no	—
214	C₄⋊C₁₆	—	7	1	no	—
215	C₄⋊C₁₆	—	7	1	no	—
216	C₄⋊C₁₆	—	7	1	no	—
217	C₄⋊C₁₆	—	7	1	no	—
218	C₄⋊C₁₆	—	7	1	no	—
219	C₂²⋊C₁₆	—	7	1	no	—
220	C₂²⋊C₁₆	—	7	1	no	—
221	C₂²⋊C₁₆	—	7	1	no	—
222	C₂²⋊C₁₆	—	7	1	no	—
223	C₂²⋊C₁₆	—	7	1	no	—
224	C₂²⋊C₁₆	—	7	1	no	—
225	#346	—	7	1	no	—
226	#346	—	7	1	no	—
227	#346	C₂×D₇	1	1	yes	characteristic
228	#346	C₂×D₇	1	1	yes	characteristic
229	C₄×C₁₆	—	7	1	no	—
230	C₄×C₁₆	—	7	1	no	—
231	C₄×C₁₆	—	7	1	no	—
232	C₄×C₁₆	—	7	1	no	—
233	C₄×C₁₆	C₂×D₇	1	1	yes	characteristic
234	C₄×C₁₆	C₂×D₇	1	1	yes	characteristic
235	C₂³×C₇	C₂²×C₈	1	1	yes	characteristic
236	C₂²×D₇	C₂²×C₈	1	1	yes	characteristic
237	C₂²×D₇	C₂²×C₈	1	1	yes	characteristic
238	C₂×C₄×C₇	—	2	1	no	—
239	C₂×C₄×C₇	—	2	1	no	—
240	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
245	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
246	C₂²⋊D₇	—	2	2	no	—
247	C₂²⋊D₇	—	2	2	no	—
248	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
249	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
250	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
251	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
252	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
253	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
254	D₂₈	—	2	2	no	—
255	C₄×D₇	—	2	2	no	—
256	C₄×D₇	—	2	1	no	—
257	C₄×D₇	—	2	1	no	—
258	C₄×D₇	—	2	1	no	—
259	C₄×D₇	—	2	1	no	—
260	C₄×D₇	—	2	2	no	—
261	Dic₁₄	—	2	2	no	—
262	C₇×C₈	—	2	1	no	—
263	C₇×C₈	—	2	1	no	—
264	C₇×C₈	#131	1	2	yes	—
265	C₇×C₈	C₂×#41	1	1	yes	characteristic
266	C₇×C₈	C₂×#41	1	1	yes	characteristic
267	C₇⋊C₈	—	2	1	no	—
268	C₇⋊C₈	—	2	1	no	—
269	C₇⋊C₈	—	2	1	no	—
270	C₇⋊C₈	—	2	1	no	—
271	C₂×M₁₆	—	7	1	no	—
272	C₂×M₁₆	C₄×D₇	1	1	yes	characteristic
273	C₂²×C₈	—	7	1	no	—
274	C₂²×C₈	—	7	1	no	—
275	C₂²×C₈	—	7	1	no	—
276	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
277	#126	—	7	1	no	—
278	#126	—	7	1	no	—
279	#125	—	7	1	no	—
280	#124	—	7	1	no	—
281	#123	—	7	1	no	—
282	#123	—	7	1	no	—
283	C₂²⋊Q₈	—	7	1	no	—
284	#121	—	7	1	no	—
285	C₄×Q₈	—	7	1	no	—
286	C₄×D₄	—	7	1	no	—
287	C₄×D₄	—	7	1	no	—
288	C₄×D₄	—	7	1	no	—
289	#117	—	7	1	no	—
290	#117	C₄×D₇	1	1	yes	characteristic
291	C₂×C₄²	—	7	1	no	—
292	M₃₂	—	2	2	no	—
293	M₃₂	—	14	2	no	—
294	C₂×C₁₆	—	2	2	no	—
295	C₂×C₁₆	—	7	1	no	—
296	C₂×C₁₆	—	7	1	no	—
297	C₂×C₁₆	—	7	1	no	—
298	C₂×C₁₆	—	7	1	no	—
299	C₂×C₁₆	—	14	2	no	—
300	C₂×C₁₆	—	14	2	no	—
301	C₂×C₁₆	—	14	2	no	—
302	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
303	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
304	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
306	C₄⋊C₈	—	7	1	no	—
307	C₄⋊C₈	—	7	1	no	—
308	C₄⋊C₈	—	7	1	no	—
309	C₄⋊C₈	—	7	1	no	—
310	C₄⋊C₈	—	7	1	no	—
311	C₄⋊C₈	—	7	1	no	—
312	C₂²⋊C₈	—	7	1	no	—
313	C₂²⋊C₈	—	7	1	no	—
314	C₂²⋊C₈	—	7	1	no	—
315	C₂²⋊C₈	—	7	1	no	—
316	C₂²⋊C₈	—	7	1	no	—
317	C₂²⋊C₈	—	7	1	no	—
318	#97	—	7	1	no	—
319	#97	—	7	1	no	—
320	#97	C₄×D₇	1	1	yes	characteristic
321	#97	C₄×D₇	1	1	yes	characteristic
322	C₄×C₈	—	7	1	no	—
323	C₄×C₈	—	7	1	no	—
324	C₄×C₈	—	7	1	no	—
325	C₄×C₈	—	7	1	no	—
326	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
328	C₂²×C₇	—	2	1	no	—
329	C₂²×C₇	—	2	1	no	—
330	C₂²×C₇	—	2	1	no	—
331	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
332	C₂×D₇	—	2	1	no	—
333	C₂×D₇	—	2	1	no	—
334	C₂×D₇	—	2	1	no	—
335	C₂×D₇	—	2	1	no	—
336	C₂×D₇	—	2	1	no	—
337	C₂×D₇	#504	1	2	yes	—
338	C₄×C₇	—	2	1	no	—
339	C₄×C₇	—	2	1	no	—
340	C₄×C₇	—	2	1	no	—
341	C₄×C₇	—	2	1	no	—
342	C₄×C₇	—	2	1	no	—
343	C₄×C₇	C₄×#41	1	1	yes	characteristic
344	C₄×C₇	C₂×#131	1	1	yes	characteristic
345	Dic₇	—	2	1	no	—
346	Dic₇	—	2	1	no	—
347	Dic₇	—	2	1	no	—
348	Dic₇	—	2	1	no	—
349	Dic₇	—	2	1	no	—
350	Dic₇	#504	1	2	yes	—
351	C₂×Q₈	—	7	1	no	—
352	C₂×D₄	—	7	1	no	—
353	C₂×D₄	—	7	1	no	—
354	C₂×D₄	—	7	1	no	—
355	C₂²×C₄	—	7	1	no	—
356	C₂²×C₄	—	7	1	no	—
357	C₂²×C₄	—	7	1	no	—
358	C₂²×C₄	—	7	1	no	—
359	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
360	M₁₆	—	2	2	no	—
361	M₁₆	—	14	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	7	1	no	—
365	C₂×C₈	—	7	1	no	—
366	C₂×C₈	—	7	1	no	—
367	C₂×C₈	—	7	1	no	—
368	C₂×C₈	—	14	2	no	—
369	C₂×C₈	—	14	1	no	—
370	C₂×C₈	—	14	1	no	—
371	C₂×C₈	—	14	1	no	—
372	C₂×C₈	—	14	1	no	—
373	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
374	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
375	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
376	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
377	C₄⋊C₄	—	7	1	no	—
378	C₄⋊C₄	—	7	1	no	—
379	C₄⋊C₄	—	7	1	no	—
380	C₄⋊C₄	—	7	1	no	—
381	C₄⋊C₄	—	7	1	no	—
382	C₄⋊C₄	—	7	1	no	—
383	C₄⋊C₄	—	7	1	no	—
384	C₄⋊C₄	—	7	1	no	—
385	C₄⋊C₄	C₈×D₇	1	1	yes	characteristic
386	C₄⋊C₄	C₈×D₇	1	1	yes	characteristic
387	C₂²⋊C₄	—	7	1	no	—
388	C₂²⋊C₄	—	7	1	no	—
389	C₂²⋊C₄	—	7	1	no	—
390	C₂²⋊C₄	—	7	1	no	—
391	C₂²⋊C₄	—	7	1	no	—
392	C₂²⋊C₄	—	7	1	no	—
393	C₂²⋊C₄	—	7	1	no	—
394	C₂²⋊C₄	—	7	1	no	—
395	C₂²⋊C₄	C₈×D₇	1	1	yes	characteristic
396	C₂²⋊C₄	C₈×D₇	1	1	yes	characteristic
397	C₄²	—	7	1	no	—
398	C₄²	—	7	1	no	—
399	C₄²	—	7	1	no	—
400	C₄²	—	7	1	no	—
401	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
402	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
403	C₁₆	—	2	1	no	—
404	C₁₆	—	2	1	no	—
405	C₁₆	—	14	1	no	—
406	C₁₆	—	14	1	no	—
407	C₁₆	—	14	1	no	—
408	C₁₆	—	14	1	no	—
409	C₁₆	#1157	1	2	yes	—
410	C₁₆	#1157	1	2	yes	—
411	C₂×C₇	—	4	1	no	—
412	C₂×C₇	C₈×#41	1	1	yes	characteristic
413	C₂×C₇	C₂×#504	1	1	yes	characteristic
414	C₂×C₇	C₂×#504	1	1	yes	characteristic
415	D₇	—	2	2	no	—
416	D₇	—	4	1	no	—
417	C₂³	—	7	1	no	—
418	C₂³	—	7	1	no	—
419	C₂³	C₂×C₈×D₇	1	1	yes	characteristic
420	Q₈	—	14	2	no	—
421	D₄	—	14	2	no	—
422	D₄	—	14	2	no	—
423	D₄	—	14	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	7	1	no	—
427	C₂×C₄	—	7	1	no	—
428	C₂×C₄	—	7	1	no	—
429	C₂×C₄	—	7	1	no	—
430	C₂×C₄	—	7	1	no	—
431	C₂×C₄	—	7	1	no	—
432	C₂×C₄	—	14	2	no	—
433	C₂×C₄	—	14	2	no	—
434	C₂×C₄	—	14	1	no	—
435	C₂×C₄	—	14	1	no	—
436	C₂×C₄	—	14	1	no	—
437	C₂×C₄	—	14	1	no	—
438	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
439	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
440	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
441	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
442	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	14	1	no	—
447	C₈	—	14	1	no	—
448	C₈	—	14	1	no	—
449	C₈	—	14	1	no	—
450	C₈	#6464	1	2	yes	—
451	C₈	C₂×#1157	1	1	yes	characteristic
452	C₈	C₂×#1157	1	1	yes	characteristic
453	C₇	#33480	1	1	yes	characteristic, complemented, Sylow
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	7	2	no	—
458	C₂²	—	14	1	no	—
459	C₂²	—	14	1	no	—
460	C₂²	—	14	1	no	—
461	C₂²	—	14	1	no	—
462	C₂²	—	14	1	no	—
463	C₂²	C₂²×C₈×D₇	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	7	2	no	—
470	C₄	—	14	1	no	—
471	C₄	—	14	1	no	—
472	C₄	—	14	1	no	—
473	C₄	—	14	1	no	—
474	C₄	—	14	1	no	—
475	C₄	C₄×#1157	1	1	yes	characteristic
476	C₄	C₂×#6464	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	14	2	no	—
479	C₂	—	28	1	no	—
480	C₂	C₈×#1157	1	1	yes	characteristic
481	C₂	D₇×#504	1	1	yes	characteristic
482	C₂	D₇×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₇
commutator, socle	C₂²×C₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₇
Fitting	C₇×#2108	C₂
prime radical	#6447	C₈
cosocle	C₂×C₇×C₈	C₂⁴
hypercenter	#2108	D₇
hypocenter	C₇	#33480
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₁₆ ◁ #2108

Complements

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

N	H ≅ G/N	type
2. C₇×#2108	C₂	semidirect
3. #11729187	C₂	semidirect
4. #11729184	C₂	semidirect
5. C₁₆×C₂²⋊D₇	C₂	semidirect
6. C₁₆×C₂²⋊D₇	C₂	semidirect
7. #11727637	C₂	semidirect
8. #11726829	C₂	semidirect
9. #11726828	C₂	semidirect
10. #11726827	C₂	semidirect
11. #11726822	C₂	semidirect
12. C₁₆×D₂₈	C₂	semidirect
13. #11726805	C₂	semidirect
14. C₄×D₇×C₁₆	C₂	semidirect
15. C₁₆×Dic₁₄	C₂	semidirect
130. #2108	D₇	semidirect
453. C₇	#33480	semidirect

Maximal subgroups

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

subgroup	index
#11736001	2
C₇×#2108	2
#11729187	2
#11729184	2
C₁₆×C₂²⋊D₇	2
#11727637	2
#11726829	2
#11726828	2
#11726827	2
#11726822	2
C₁₆×D₂₈	2
#11726805	2
C₄×D₇×C₁₆	2
C₁₆×Dic₁₄	2
#33480	7