Subgroups — C₈×#14519864 #30609685

Order 15616.

922 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462624	C₂	1	1	yes	maximal, characteristic
2	C₄×#14519864	C₂	1	1	yes	maximal, characteristic
3	#21461025	C₂	1	1	yes	maximal, characteristic, complemented
4	#21461024	C₂	1	2	yes	maximal, complemented
5	#21461021	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461020	C₂	1	2	yes	maximal, complemented
7	C₈×#11758213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#11758217	C₂	1	2	yes	maximal, complemented
9	C₈×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×#92420	C₂	1	2	yes	maximal, complemented
11	C₈×#11758224	C₂	1	1	yes	maximal, characteristic
12	C₂×#14519864	C₄	1	2	yes	—
13	#16840811	C₄	1	2	yes	—
14	#16840789	C₄	1	4	yes	—
15	D₄×#92420	C₄	1	2	yes	—
16	#16840781	C₂²	1	1	yes	characteristic
17	#16840779	C₂²	1	2	yes	—
18	#16840727	C₄	1	2	yes	—
19	#16840726	C₄	1	4	yes	—
20	C₄×#11758213	C₂²	1	1	yes	characteristic
21	C₄×#11758217	C₂²	1	2	yes	—
22	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
23	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×#92420	C₂²	1	2	yes	—
25	C₂×C₄×#92420	C₂²	1	2	yes	—
26	#92420⋊C₈	C₂²	1	2	yes	—
27	#92420⋊C₈	C₂²	1	2	yes	—
28	#92420⋊C₈	C₂²	1	2	yes	—
29	C₈×#92420	C₂²	1	1	yes	characteristic
30	C₈×#92420	C₂²	1	2	yes	—
31	C₈×#92420	C₂²	1	2	yes	—
32	C₈×#92420	C₂²	1	2	yes	—
33	C₈×#92420	C₂²	1	1	yes	characteristic
34	C₈×#92420	C₂²	1	1	yes	characteristic
35	C₈×#92420	C₂²	1	1	yes	characteristic
36	C₄×#11758224	C₂²	1	1	yes	characteristic
37	C₈×Dic₁₂₂	C₄	1	1	yes	characteristic
38	#16839886	C₄	1	1	yes	characteristic
39	D₄×#92418	C₄	1	1	yes	characteristic
40	C₈×C₂²⋊D₆₁	C₄	1	2	yes	—
41	#16839825	C₄	1	2	yes	—
42	#16839814	C₂²	1	1	yes	characteristic
43	#16839812	C₂²	1	2	yes	—
44	C₂×C₈×Dic₆₁	C₂²	1	2	yes	—
45	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
46	C₈×D₄×C₆₁	C₄	1	1	yes	characteristic
47	#14519864	C₈	1	16	yes	direct product factor
48	C₂×#11758213	C₂×C₄	1	2	yes	—
49	C₂×#11758217	C₂×C₄	1	4	yes	—
50	C₂×D₆₁⋊C₈	C₂×C₄	1	2	yes	—
51	C₂×D₆₁⋊C₈	C₂×C₄	1	2	yes	—
52	C₂²×#92420	C₂×C₄	1	4	yes	—
53	C₂²×#92420	C₂×C₄	1	4	yes	—
54	#14519844	C₂×C₄	1	4	yes	—
55	C₄⋊#92420	C₂×C₄	1	2	yes	—
56	#14519834	C₂×C₄	1	2	yes	—
57	C₂²⋊#92420	C₂×C₄	1	4	yes	—
58	#14519832	C₂×C₄	1	4	yes	—
59	#14519832	C₂×C₄	1	2	yes	—
60	C₄×#92420	C₂×C₄	1	4	yes	—
61	C₄×#92420	C₂×C₄	1	4	yes	—
62	C₄×#92420	C₂×C₄	1	2	yes	—
63	C₄×#92420	C₂×C₄	1	2	yes	—
64	C₄×#92420	C₂³	1	1	yes	characteristic
65	C₄×#92420	C₂³	1	1	yes	characteristic
66	C₄×#92420	C₂³	1	2	yes	—
67	C₄×#92420	C₂³	1	2	yes	—
68	C₄×#92420	C₂³	1	1	yes	characteristic
69	C₄×#92420	C₂³	1	1	yes	characteristic
70	C₂×#11758224	C₂×C₄	1	1	yes	characteristic
71	C₂²×#92418	C₂×C₄	1	2	yes	—
72	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
74	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
75	#14519742	C₂×C₄	1	1	yes	characteristic
76	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₆₁	C₂×C₄	1	2	yes	—
78	#14519737	C₂×C₄	1	2	yes	—
79	#14519735	C₂×C₄	1	1	yes	characteristic
80	#14519733	C₂×C₄	1	2	yes	—
81	C₂×C₄×Dic₆₁	C₂³	1	2	yes	—
82	C₄²×D₆₁	C₂³	1	1	yes	characteristic
83	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
84	#14519706	C₂×C₄	1	2	yes	—
85	#14519706	C₂×C₄	1	2	yes	—
86	C₂²⋊#92418	C₂×C₄	1	2	yes	—
87	#14519689	C₂×C₄	1	2	yes	—
88	C₄×#92418	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
90	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
91	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
92	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
93	C₈×Dic₆₁	C₂³	1	2	yes	—
94	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
95	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
96	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
98	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
99	C₂×D₄×C₆₁	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
101	C₂×C₂²⋊D₆₁	C₄²	1	2	yes	—
102	C₂²×Dic₆₁	C₂²×C₄	1	2	yes	—
103	C₂²×Dic₆₁	C₂²×C₄	1	2	yes	—
104	#11758224	C₂×C₈	1	8	yes	—
105	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×Dic₁₂₂	C₄²	1	1	yes	characteristic
109	#11758217	C₂×C₈	1	16	yes	complemented
110	C₂×#92420	—	2	8	no	—
111	C₂×#92420	C₂×C₈	1	16	yes	complemented
112	C₂×#92420	C₂²×C₄	1	2	yes	—
113	C₂×#92420	C₂²×C₄	1	4	yes	—
114	C₂×#92420	C₂²×C₄	1	2	yes	—
115	C₂×#92420	C₂²×C₄	1	4	yes	—
116	C₂×#92420	C₂²×C₄	1	2	yes	—
117	C₂×#92420	C₂²×C₄	1	2	yes	—
118	#11758213	C₂×C₈	1	8	yes	complemented
119	D₆₁⋊C₈	—	2	4	no	—
120	D₆₁⋊C₈	C₂×C₈	1	8	yes	complemented
121	C₂×C₈×C₆₁	—	2	4	no	—
122	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
125	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
126	C₂²⋊C₄×C₆₁	C₄²	1	2	yes	—
127	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²⋊Dic₆₁	C₄²	1	2	yes	—
129	#11758198	C₄²	1	2	yes	—
130	C₄⋊Dic₆₁	C₄²	1	1	yes	characteristic
131	#11758196	C₄²	1	2	yes	—
132	#11758196	C₄²	1	2	yes	—
133	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
134	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
136	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
138	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
139	C₂×#92418	—	2	4	no	—
140	C₂×#92418	C₂²×C₄	1	2	yes	—
141	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
142	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
143	C₈×D₆₁	—	2	2	no	—
144	C₈×D₆₁	—	2	2	no	—
145	C₂³×C₆₁	C₂×C₄²	1	2	yes	—
146	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
147	D₄×C₆₁	C₄×C₈	1	4	yes	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	2	no	—
150	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
154	C₂²⋊D₆₁	C₄×C₈	1	8	yes	—
155	C₂×Dic₆₁	—	2	4	no	—
156	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
157	C₂×Dic₆₁	C₂×C₄²	1	2	yes	—
158	C₂×Dic₆₁	C₂×C₄²	1	2	yes	—
159	C₂×Dic₆₁	C₂²×C₈	1	8	yes	—
160	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
162	C₄×D₆₁	—	2	1	no	—
163	C₄×D₆₁	—	2	1	no	—
164	C₄×D₆₁	—	2	2	no	—
165	C₄×D₆₁	C₂²×C₈	1	4	yes	—
166	Dic₁₂₂	C₄×C₈	1	4	yes	—
167	#92420	—	2	2	no	—
168	#92420	—	2	4	no	—
169	#92420	C₂²×C₈	1	4	yes	—
170	#92420	C₂²×C₈	1	4	yes	—
171	#92420	C₂²×C₈	1	8	yes	—
172	#92420	#131	1	4	yes	complemented
173	C₈×C₆₁	—	2	1	no	—
174	C₈×C₆₁	—	2	2	no	—
175	C₈×C₆₁	#131	1	2	yes	complemented
176	#92418	—	2	1	no	—
177	#92418	—	2	2	no	—
178	#92418	#131	1	2	yes	complemented
179	C₈×#131	—	61	1	no	maximal, Sylow
180	C₂²×C₆₁	—	2	2	no	—
181	C₂²×C₆₁	—	2	2	no	—
182	C₂²×C₆₁	C₂×C₄×C₈	1	4	yes	—
183	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
184	C₂×D₆₁	—	2	1	no	—
185	C₂×D₆₁	—	2	1	no	—
186	C₂×D₆₁	C₂×C₄×C₈	1	2	yes	—
187	C₄×C₆₁	—	2	1	no	—
188	C₄×C₆₁	—	2	2	no	—
189	C₄×C₆₁	C₂×C₄×C₈	1	2	yes	—
190	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
191	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
192	Dic₆₁	—	2	1	no	—
193	Dic₆₁	—	2	2	no	—
194	Dic₆₁	C₂×C₄×C₈	1	4	yes	—
195	Dic₆₁	C₂³×C₈	1	2	yes	—
196	Dic₆₁	C₂×#131	1	2	yes	—
197	C₈×#41	—	61	1	no	—
198	C₈×#41	—	61	1	no	—
199	C₄×#131	—	61	1	no	—
200	#1450	—	61	2	no	—
201	#1450	—	61	1	no	—
202	C₈×M₁₆	—	61	2	no	—
203	C₈×M₁₆	—	61	1	no	—
204	C₈×M₁₆	—	61	2	no	—
205	C₈×M₁₆	—	61	1	no	—
206	C₂×C₈²	—	61	2	no	—
207	C₂×C₈²	—	61	1	no	—
208	C₂×C₆₁	—	2	4	no	—
209	C₂×C₆₁	C₂²×C₄×C₈	1	1	yes	characteristic
210	C₂×C₆₁	C₄×#131	1	1	yes	characteristic
211	C₂×C₆₁	C₄×#131	1	1	yes	characteristic
212	D₆₁	—	2	2	no	—
213	C₂×#131	—	61	2	no	—
214	C₄×#41	—	61	1	no	—
215	C₈×Q₈	—	61	2	no	—
216	C₈×Q₈	—	61	1	no	—
217	C₈×Q₈	—	61	1	no	—
218	C₈×D₄	—	61	2	no	—
219	C₈×D₄	—	61	4	no	—
220	C₈×D₄	—	61	2	no	—
221	C₈×D₄	—	61	1	no	—
222	C₈×D₄	—	61	2	no	—
223	C₈×D₄	#6923	1	1	yes	characteristic
224	#431	—	61	2	no	—
225	#431	—	61	1	no	—
226	#431	—	61	1	no	—
227	#431	—	61	2	no	—
228	#405	—	61	4	no	—
229	#405	—	61	2	no	—
230	C₄×M₁₆	—	61	2	no	—
231	C₄×M₁₆	—	61	1	no	—
232	C₂×C₄×C₈	—	61	2	no	—
233	C₂×C₄×C₈	—	61	2	no	—
234	C₂×C₄×C₈	—	61	1	no	—
235	C₂×C₄×C₈	—	61	1	no	—
236	C₂×C₄×C₈	—	61	2	no	—
237	C₂×C₄×C₈	—	61	1	no	—
238	#322	—	61	2	no	—
239	#322	—	61	2	no	—
240	#322	—	61	2	no	—
241	C₈²	—	61	1	no	—
242	C₈²	—	61	2	no	—
243	C₈²	—	61	1	no	—
244	C₈²	—	61	2	no	—
245	C₈²	—	61	1	no	—
246	C₈²	—	61	2	no	—
247	C₈²	—	61	1	no	—
248	C₆₁	C₈×#131	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	61	1	no	—
250	#131	—	61	16	no	—
251	C₂×M₁₆	—	61	4	no	—
252	C₂×M₁₆	—	61	2	no	—
253	C₂²×C₈	—	61	4	no	—
254	C₂²×C₈	—	61	2	no	—
255	C₂²×C₈	—	61	4	no	—
256	C₂²×C₈	—	61	2	no	—
257	C₂²×C₈	—	61	2	no	—
258	C₂²×C₈	—	61	1	no	—
259	C₂²×C₈	—	61	1	no	—
260	C₂²×C₈	C₂×#6923	1	2	yes	—
261	C₄×Q₈	—	61	1	no	—
262	C₄×Q₈	—	61	1	no	—
263	C₄×D₄	—	61	1	no	—
264	C₄×D₄	—	61	2	no	—
265	C₄×D₄	—	61	2	no	—
266	C₄×D₄	C₂×#6923	1	1	yes	characteristic
267	#117	—	61	1	no	—
268	#117	—	61	2	no	—
269	C₂×C₄²	—	61	2	no	—
270	C₂×C₄²	—	61	1	no	—
271	C₄⋊C₈	—	61	2	no	—
272	C₄⋊C₈	—	61	4	no	—
273	C₄⋊C₈	—	61	2	no	—
274	C₄⋊C₈	—	61	2	no	—
275	C₄⋊C₈	—	61	1	no	—
276	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic
277	C₂²⋊C₈	—	61	4	no	—
278	C₂²⋊C₈	—	61	2	no	—
279	C₂²⋊C₈	—	61	2	no	—
280	C₂²⋊C₈	—	61	2	no	—
281	C₂²⋊C₈	C₂×#6923	1	2	yes	—
282	#97	—	61	4	no	—
283	#97	—	61	2	no	—
284	C₄×C₈	—	61	4	no	—
285	C₄×C₈	—	61	2	no	—
286	C₄×C₈	—	61	4	no	—
287	C₄×C₈	—	61	2	no	—
288	C₄×C₈	—	61	1	no	—
289	C₄×C₈	—	61	1	no	—
290	C₄×C₈	—	61	2	no	—
291	C₄×C₈	—	61	1	no	—
292	C₄×C₈	—	61	2	no	—
293	C₄×C₈	—	61	1	no	—
294	C₄×C₈	—	61	2	no	—
295	C₄×C₈	—	61	1	no	—
296	C₄×C₈	—	61	2	no	—
297	C₄×C₈	—	61	1	no	—
298	C₄×C₈	—	61	2	no	—
299	C₄×C₈	—	61	1	no	—
300	C₄×C₈	C₂×#6923	1	1	yes	characteristic
301	#41	—	61	8	no	—
302	C₂×Q₈	—	61	1	no	—
303	C₂×D₄	—	61	2	no	—
304	C₂×D₄	C₄×#6923	1	1	yes	characteristic
305	C₂²×C₄	—	61	2	no	—
306	C₂²×C₄	—	61	1	no	—
307	C₂²×C₄	—	61	2	no	—
308	C₂²×C₄	—	61	1	no	—
309	C₂²×C₄	—	61	1	no	—
310	C₂²×C₄	C₂²×#6923	1	2	yes	—
311	M₁₆	—	61	8	no	—
312	M₁₆	—	61	16	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	61	2	no	—
315	C₂×C₈	—	61	2	no	—
316	C₂×C₈	—	61	4	no	—
317	C₂×C₈	—	61	2	no	—
318	C₂×C₈	—	61	8	no	—
319	C₂×C₈	—	61	16	no	—
320	C₂×C₈	—	61	1	no	—
321	C₂×C₈	—	61	2	no	—
322	C₂×C₈	—	61	4	no	—
323	C₂×C₈	—	61	1	no	—
324	C₂×C₈	—	61	2	no	—
325	C₂×C₈	—	122	2	no	—
326	C₂×C₈	—	122	4	no	—
327	C₂×C₈	—	122	4	no	—
328	C₂×C₈	—	122	8	no	—
329	C₂×C₈	—	122	2	no	—
330	C₂×C₈	C₂²×#6923	1	2	yes	—
331	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
332	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
333	C₄⋊C₄	—	61	2	no	—
334	C₄⋊C₄	—	61	2	no	—
335	C₄⋊C₄	—	61	1	no	—
336	C₄⋊C₄	C₄×#6923	1	1	yes	characteristic
337	C₂²⋊C₄	—	61	2	no	—
338	C₂²⋊C₄	—	61	2	no	—
339	C₂²⋊C₄	C₄×#6923	1	2	yes	—
340	C₄²	—	61	2	no	—
341	C₄²	—	61	1	no	—
342	C₄²	—	61	2	no	—
343	C₄²	—	61	1	no	—
344	C₄²	—	61	1	no	—
345	C₄²	—	61	2	no	—
346	C₄²	C₂²×#6923	1	1	yes	characteristic
347	C₂³	—	61	1	no	—
348	C₂³	C₂×C₄×#6923	1	2	yes	—
349	Q₈	—	61	4	no	—
350	D₄	—	61	8	no	—
351	D₄	C₈×#6923	1	4	yes	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	61	8	no	—
355	C₂×C₄	—	61	2	no	—
356	C₂×C₄	—	61	1	no	—
357	C₂×C₄	—	61	1	no	—
358	C₂×C₄	—	61	4	no	—
359	C₂×C₄	—	61	2	no	—
360	C₂×C₄	—	61	1	no	—
361	C₂×C₄	—	122	2	no	—
362	C₂×C₄	—	122	4	no	—
363	C₂×C₄	—	122	1	no	—
364	C₂×C₄	—	122	1	no	—
365	C₂×C₄	C₂×C₄×#6923	1	2	yes	—
366	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
368	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
369	C₈	—	2	2	no	—
370	C₈	—	2	1	no	—
371	C₈	—	61	4	no	—
372	C₈	—	61	4	no	—
373	C₈	—	61	8	no	—
374	C₈	—	61	4	no	—
375	C₈	—	61	2	no	—
376	C₈	—	122	2	no	—
377	C₈	—	122	4	no	—
378	C₈	—	122	1	no	—
379	C₈	—	122	2	no	—
380	C₈	#14519864	1	2	yes	direct product factor
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	61	2	no	—
384	C₂²	—	122	1	no	—
385	C₂²	—	122	1	no	—
386	C₂²	C₂×C₈×#6923	1	4	yes	—
387	C₂²	C₂²×C₄×#6923	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	61	2	no	—
391	C₄	—	61	4	no	—
392	C₄	—	61	2	no	—
393	C₄	—	122	2	no	—
394	C₄	—	122	1	no	—
395	C₄	C₂×C₈×#6923	1	2	yes	—
396	C₄	C₂×#14519864	1	1	yes	characteristic
397	C₄	D₆₁⋊#131	1	1	yes	characteristic
398	C₂	—	2	4	no	—
399	C₂	—	122	2	no	—
400	C₂	C₂²×C₈×#6923	1	1	yes	characteristic
401	C₂	#131×#6923	1	1	yes	characteristic
402	C₂	C₄×#14519864	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#6923
commutator	C₂×C₆₁	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₈×D₄×C₆₁	C₄
socle	C₂²×C₆₁	C₂²×C₄²
prime radical	C₂×#11758224	C₂×C₄
cosocle	C₄×Dic₆₁	C₂⁴
hypercenter	C₈×D₄	#6923
hypocenter	C₆₁	C₈×#131
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
3. #21461025	C₂	semidirect
4. #21461024	C₂	semidirect
5. #21461021	C₂	semidirect
6. #21461020	C₂	semidirect
7. C₈×#11758213	C₂	semidirect
8. C₈×#11758217	C₂	semidirect
9. C₈×D₆₁⋊C₈	C₂	semidirect
10. C₂×C₈×#92420	C₂	semidirect
47. #14519864	C₈	direct (N × H)
109. #11758217	C₂×C₈	semidirect
111. C₂×#92420	C₂×C₈	semidirect
118. #11758213	C₂×C₈	semidirect
120. D₆₁⋊C₈	C₂×C₈	semidirect
172. #92420	#131	semidirect
175. C₈×C₆₁	#131	semidirect
178. #92418	#131	semidirect
248. C₆₁	C₈×#131	semidirect
380. C₈	#14519864	direct (N × H)

Maximal subgroups

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

subgroup	index
#21462624	2
C₄×#14519864	2
#21461025	2
#21461024	2
#21461021	2
#21461020	2
C₈×#11758213	2
C₈×#11758217	2
C₈×D₆₁⋊C₈	2
C₂×C₈×#92420	2
C₈×#11758224	2
C₈×#131	61

Subgroups — C8×#14519864 #30609685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#14519864 #30609685