Subgroups — C₄×#15689564 #26369607

Order 12032.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689564	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094046	C₂	1	1	yes	maximal, characteristic
3	#20245257	C₂	1	2	yes	maximal, complemented
4	#20245250	C₂	1	2	yes	maximal, complemented
5	C₄×#13093970	C₂	1	2	yes	maximal, complemented
6	C₄×#13093967	C₂	1	2	yes	maximal, complemented
7	#20245174	C₂	1	1	yes	maximal, characteristic, complemented
8	#20245108	C₂	1	1	yes	maximal, characteristic, complemented
9	#20245098	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093964	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₄×#10625350	—	2	1	no	—
14	#15689564	C₄	1	8	yes	direct product factor
15	C₂×#13093970	C₂²	1	2	yes	—
16	C₂×#13093967	C₂²	1	2	yes	—
17	C₂×#13093964	C₂²	1	1	yes	characteristic
18	C₂×#13093964	C₂²	1	1	yes	characteristic
19	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic
20	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic
21	C₄×#10625325	—	2	1	no	—
22	C₄×#10625325	—	2	1	no	—
23	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
24	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
25	#15689161	C₂²	1	1	yes	characteristic
26	#15689120	—	2	1	no	—
27	#15688950	C₂²	1	2	yes	—
28	#15688948	C₂²	1	2	yes	—
29	#15688927	C₂²	1	2	yes	—
30	#15688927	C₂²	1	2	yes	—
31	#15688926	C₂²	1	2	yes	—
32	#15688923	C₂²	1	2	yes	—
33	#15688899	C₂²	1	2	yes	—
34	C₄×C₄₇⋊C₁₆	C₂²	1	2	yes	—
35	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
37	C₄×Q₁₆×C₄₇	—	2	1	no	—
38	C₄×Q₁₆×C₄₇	—	2	1	no	—
39	C₄×Q₁₆×C₄₇	C₂²	1	2	yes	—
40	C₄×Q₁₆×C₄₇	C₂²	1	2	yes	—
41	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₄₇	—	2	1	no	—
43	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#10625350	—	2	1	no	—
45	#13094046	—	2	2	no	—
46	#13094046	C₂×C₄	1	4	yes	—
47	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
48	C₂×#10625325	—	2	1	no	—
49	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
50	C₄×Dic₉₄	—	2	1	no	—
51	C₄×Dic₉₄	—	2	1	no	—
52	C₄×D₁₈₈	—	2	1	no	—
53	C₄×D₁₈₈	—	2	1	no	—
54	C₄×C₂²⋊D₄₇	—	4	1	no	—
55	C₄×C₂²⋊D₄₇	—	4	1	no	—
56	#13093983	—	2	1	no	—
57	#13093981	—	4	1	no	—
58	C₄²×D₄₇	—	4	1	no	—
59	#13093970	C₂×C₄	1	8	yes	complemented
60	#13093967	C₂×C₄	1	8	yes	complemented
61	#13093964	—	2	2	no	—
62	#13093964	C₂×C₄	1	4	yes	complemented
63	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
64	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
65	#13093958	C₂³	1	1	yes	characteristic
66	#13093958	C₂³	1	1	yes	characteristic
67	#13093956	—	2	1	no	—
68	#13093949	—	2	1	no	—
69	#13093949	—	2	1	no	—
70	#13093946	—	2	1	no	—
71	#13093946	—	2	1	no	—
72	C₂²×Q₈×C₄₇	—	2	1	no	—
73	C₂×Q₁₆×C₄₇	—	2	1	no	—
74	C₂×Q₁₆×C₄₇	—	2	2	no	—
75	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
76	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₄×Q₈×C₄₇	—	2	2	no	—
80	C₄×Q₈×C₄₇	—	2	2	no	—
81	C₄×Q₈×C₄₇	—	4	1	no	—
82	C₄×Q₈×C₄₇	—	4	1	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
85	C₂×C₄²×C₄₇	—	4	1	no	—
86	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
87	#107×C₄₇	—	2	1	no	—
88	#107×C₄₇	C₂³	1	2	yes	—
89	#103×C₄₇	—	2	2	no	—
90	#103×C₄₇	—	2	2	no	—
91	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
92	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×Q₈×C₄₇	—	2	4	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	4	1	no	—
98	C₂×Q₈×C₄₇	—	4	2	no	—
99	C₂²×C₄×C₄₇	—	4	1	no	—
100	C₂²×C₄×C₄₇	—	4	1	no	—
101	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₇	—	4	1	no	—
105	#10625350	—	2	4	no	—
106	#10625350	—	4	2	no	—
107	C₂×D₁₈₈	—	2	1	no	—
108	C₂×C₄×D₄₇	—	4	1	no	—
109	C₂×C₄×D₄₇	—	4	1	no	—
110	C₂×C₄×D₄₇	—	4	1	no	—
111	C₂×Dic₉₄	—	2	1	no	—
112	Q₁₆×C₄₇	—	2	4	no	—
113	Q₁₆×C₄₇	—	2	2	no	—
114	Q₁₆×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	#41	1	2	yes	—
121	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	4	1	no	—
124	C₄⋊C₄×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	—	4	2	no	—
126	C₄²×C₄₇	—	4	2	no	—
127	C₄²×C₄₇	—	4	2	no	—
128	C₄²×C₄₇	D₈	1	1	yes	characteristic
129	C₄²×C₄₇	D₈	1	1	yes	characteristic
130	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²⋊Dic₄₇	—	4	1	no	—
133	(C₂×D₄₇)⋊C₄	—	4	1	no	—
134	(C₂×D₄₇)⋊C₄	—	4	1	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	Dic₄₇⋊C₄	—	4	1	no	—
138	Dic₄₇⋊C₄	—	4	1	no	—
139	C₄×Dic₄₇	—	4	1	no	—
140	C₄×Dic₄₇	—	4	1	no	—
141	C₄×Dic₄₇	—	4	1	no	—
142	Dic₁₈₈	—	2	1	no	—
143	Dic₁₈₈	C₂²×C₄	1	2	yes	—
144	D₃₇₆	—	2	1	no	—
145	D₃₇₆	C₂²×C₄	1	2	yes	—
146	#10625325	—	2	4	no	—
147	C₄₇⋊C₁₆	—	2	2	no	—
148	C₄₇⋊C₁₆	C₂²×C₄	1	4	yes	—
149	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
150	C₂²×D₄₇	—	4	1	no	—
151	Q₈×C₄₇	—	2	4	no	—
152	Q₈×C₄₇	—	4	2	no	—
153	Q₈×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	4	1	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	8	2	no	—
160	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#135	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂²⋊D₄₇	—	4	4	no	—
169	C₂×Dic₄₇	—	4	1	no	—
170	C₂×Dic₄₇	—	4	1	no	—
171	C₂×Dic₄₇	—	4	1	no	—
172	D₁₈₈	—	2	2	no	—
173	D₁₈₈	—	4	1	no	—
174	C₄×D₄₇	—	4	4	no	—
175	C₄×D₄₇	—	8	2	no	—
176	C₄×D₄₇	—	8	2	no	—
177	Dic₉₄	—	2	2	no	—
178	Dic₉₄	—	4	1	no	—
179	C₈×C₄₇	—	2	1	no	—
180	C₈×C₄₇	—	2	1	no	—
181	C₈×C₄₇	C₄×D₄	1	2	yes	—
182	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₄×#510	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	C₄×D₈	1	2	yes	—
188	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
189	C₂×D₄₇	—	4	2	no	—
190	C₂×D₄₇	—	8	1	no	—
191	C₂×D₄₇	—	8	1	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	—	8	2	no	—
197	C₄×C₄₇	C₄×D₈	1	2	yes	—
198	C₄×C₄₇	#510	1	2	yes	complemented
199	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
201	Dic₄₇	—	4	2	no	—
202	Dic₄₇	—	8	1	no	—
203	Dic₄₇	—	8	1	no	—
204	C₂×#510	—	47	1	no	—
205	C₄×#135	—	47	1	no	—
206	C₂×C₄×Q₁₆	D₄₇	1	1	yes	characteristic, complemented
207	#2176	—	47	2	no	—
208	#2175	—	47	2	no	—
209	C₄×Q₃₂	—	47	2	no	—
210	C₄×SD₃₂	—	47	2	no	—
211	#2159	—	47	1	no	—
212	#2141	—	47	1	no	—
213	#2139	—	47	1	no	—
214	C₄×M₃₂	—	47	1	no	—
215	C₂×C₄₇	—	2	2	no	—
216	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#510	1	1	yes	characteristic
218	C₂×C₄₇	#3414	1	1	yes	characteristic
219	D₄₇	—	8	2	no	—
220	C₂×#135	—	47	1	no	—
221	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
222	C₄×#41	—	94	1	no	—
223	C₂×C₄×Q₈	—	2	1	no	—
224	#510	—	47	8	no	—
225	C₂×Q₃₂	—	47	2	no	—
226	C₂×SD₃₂	—	47	2	no	—
227	C₂×M₃₂	—	47	1	no	—
228	C₂×M₃₂	—	47	1	no	—
229	C₄×Q₁₆	—	2	1	no	—
230	C₄×Q₁₆	—	2	1	no	—
231	C₄×Q₁₆	—	47	1	no	—
232	C₄×Q₁₆	—	47	1	no	—
233	C₄×Q₁₆	C₂×D₄₇	1	2	yes	—
234	C₄×Q₁₆	C₂×D₄₇	1	2	yes	—
235	C₄×SD₁₆	—	94	1	no	—
236	C₄×SD₁₆	—	94	1	no	—
237	C₄×D₈	—	47	1	no	—
238	C₄×D₈	—	47	1	no	—
239	#427	—	47	1	no	—
240	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
241	#416	—	94	1	no	—
242	C₂×#103	—	2	1	no	—
243	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
244	#367	—	47	2	no	—
245	#366	—	47	2	no	—
246	#358	—	47	2	no	—
247	#358	—	47	2	no	—
248	#358	—	47	2	no	—
249	#357	—	47	2	no	—
250	#346	—	47	2	no	—
251	C₄×C₁₆	—	47	2	no	—
252	C₄₇	C₄×#510	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	94	1	no	—
254	C₂²×Q₈	—	2	1	no	—
255	#135	—	47	4	no	—
256	#135	—	94	2	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	—	2	1	no	—
259	C₂×Q₁₆	—	47	1	no	—
260	C₂×Q₁₆	C₄×D₄₇	1	4	yes	complemented
261	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
262	C₂×SD₁₆	—	94	1	no	—
263	C₂×D₈	—	47	1	no	—
264	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	—	4	1	no	—
269	C₄×Q₈	—	4	1	no	—
270	C₄×Q₈	—	94	1	no	—
271	C₄×Q₈	—	94	1	no	—
272	C₄×D₄	—	94	1	no	—
273	C₄×D₄	—	94	1	no	—
274	C₄×D₄	—	188	1	no	—
275	C₄×D₄	—	188	1	no	—
276	#117	—	94	1	no	—
277	#117	—	188	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	4	1	no	—
280	C₂×C₄²	—	4	1	no	—
281	C₂×C₄²	—	188	1	no	—
282	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
283	Q₃₂	—	47	8	no	—
284	SD₃₂	—	47	8	no	—
285	M₃₂	—	47	4	no	—
286	M₃₂	—	94	2	no	—
287	C₂×C₁₆	—	47	2	no	—
288	C₂×C₁₆	—	47	2	no	—
289	#107	—	2	1	no	—
290	#107	—	47	1	no	—
291	#107	—	47	1	no	—
292	#107	C₂²×D₄₇	1	2	yes	—
293	#106	—	94	1	no	—
294	#103	—	2	2	no	—
295	#103	—	2	2	no	—
296	#103	—	94	1	no	—
297	#103	—	94	1	no	—
298	#102	—	94	1	no	—
299	#102	—	94	1	no	—
300	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
301	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
304	#41	—	94	4	no	—
305	#41	—	188	2	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	94	1	no	—
311	C₂×D₄	—	94	1	no	—
312	C₂×D₄	—	188	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	188	1	no	—
316	C₂²×C₄	—	188	1	no	—
317	C₂²×C₄	—	188	1	no	—
318	C₂²×C₄	#10625334	1	1	yes	characteristic
319	C₂²×C₄	#10625334	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
321	Q₁₆	—	2	4	no	—
322	Q₁₆	—	2	2	no	—
323	Q₁₆	—	47	2	no	—
324	Q₁₆	—	94	1	no	—
325	Q₁₆	C₂×C₄×D₄₇	1	4	yes	—
326	SD₁₆	—	94	4	no	—
327	D₈	—	47	2	no	—
328	D₈	—	94	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
331	C₂×C₈	#10625350	1	2	yes	—
332	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
333	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
335	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	94	1	no	—
341	C₄⋊C₄	—	94	1	no	—
342	C₄⋊C₄	—	188	1	no	—
343	C₄⋊C₄	—	188	1	no	—
344	C₂²⋊C₄	—	188	1	no	—
345	C₂²⋊C₄	—	188	1	no	—
346	C₂²⋊C₄	—	188	1	no	—
347	C₄²	—	4	2	no	—
348	C₄²	—	4	2	no	—
349	C₄²	—	188	1	no	—
350	C₄²	—	188	1	no	—
351	C₄²	—	188	1	no	—
352	C₄²	#10625334	1	1	yes	characteristic
353	C₄²	#10625334	1	1	yes	characteristic
354	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
355	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₁₆	—	47	4	no	—
357	C₁₆	—	94	2	no	—
358	C₂³	—	188	1	no	—
359	C₂³	C₂×#10625334	1	1	yes	characteristic
360	Q₈	—	2	4	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	4	no	—
363	Q₈	—	94	2	no	—
364	Q₈	—	188	1	no	—
365	D₄	—	94	2	no	—
366	D₄	—	188	4	no	—
367	D₄	—	188	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	376	2	no	—
375	C₂×C₄	—	376	2	no	—
376	C₂×C₄	—	188	1	no	—
377	C₂×C₄	—	188	1	no	—
378	C₂×C₄	—	188	1	no	—
379	C₂×C₄	—	188	4	no	—
380	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
381	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
382	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
383	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
385	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
386	C₂×C₄	#13094044	1	2	yes	—
387	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
391	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
392	C₈	C₂×#10625350	1	1	yes	characteristic
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	376	1	no	—
396	C₂²	—	376	1	no	—
397	C₂²	—	188	2	no	—
398	C₂²	C₄×#10625334	1	2	yes	—
399	C₂²	C₂²×#10625334	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	—	376	1	no	—
406	C₄	—	376	1	no	—
407	C₄	—	188	2	no	—
408	C₄	C₄×#10625334	1	2	yes	—
409	C₄	#15689564	1	2	yes	direct product factor
410	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
411	C₄	C₂×#13094044	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	376	2	no	—
414	C₂	C₂×C₄×#10625334	1	1	yes	characteristic
415	C₂	C₂×#15689564	1	1	yes	characteristic
416	C₂	#20256522	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#10625334
commutator	C₈×C₄₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂×C₄×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₈
prime radical	C₂×#13094046	C₂²
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₄₇
hypocenter	C₄₇	C₄×#510
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #20245257	C₂	semidirect
4. #20245250	C₂	semidirect
5. C₄×#13093970	C₂	semidirect
6. C₄×#13093967	C₂	semidirect
7. #20245174	C₂	semidirect
8. #20245108	C₂	semidirect
10. C₄×#13093964	C₂	semidirect
11. C₂×C₄×Q₁₆×C₄₇	C₂	semidirect
14. #15689564	C₄	direct (N × H)
59. #13093970	C₂×C₄	semidirect
60. #13093967	C₂×C₄	semidirect
62. #13093964	C₂×C₄	semidirect
75. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
198. C₄×C₄₇	#510	semidirect
206. C₂×C₄×Q₁₆	D₄₇	semidirect
252. C₄₇	C₄×#510	semidirect
260. C₂×Q₁₆	C₄×D₄₇	semidirect
409. C₄	#15689564	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×#15689564	2
C₄×#13094046	2
#20245257	2
#20245250	2
C₄×#13093970	2
C₄×#13093967	2
#20245174	2
#20245108	2
#20245098	2
C₄×#13093964	2
C₂×C₄×Q₁₆×C₄₇	2
C₄×#510	47

Subgroups — C4×#15689564 #26369607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689564 #26369607