Subgroups — C₄×#15688857 #26107152

Order 12032.

816 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15688857	C₂	1	2	yes	maximal
3	C₄×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241266	C₂	1	2	yes	maximal, complemented
5	C₄×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×Dic₄₇	—	2	1	no	—
7	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
9	C₂×C₄₇⋊#95	—	2	1	no	—
10	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
11	#15688878	—	2	1	no	—
12	#15688857	C₄	1	8	yes	direct product factor
13	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₇	—	2	1	no	—
15	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic, complemented
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#390	C₄	1	1	yes	characteristic, complemented
18	C₄₇×#389	C₄	1	1	yes	characteristic, complemented
19	C₄₇×#388	—	2	1	no	—
20	C₄₇×#386	—	2	1	no	—
21	C₄₇×#380	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic, complemented
23	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
24	C₂³×Dic₄₇	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂×C₄×Dic₄₇	—	2	4	no	—
27	C₂×C₄×Dic₄₇	—	4	2	no	—
28	C₂×C₄×Dic₄₇	—	4	2	no	—
29	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
30	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
31	C₄×C₄₇⋊C₈	—	4	2	no	—
32	C₄₇⋊#95	—	2	4	no	—
33	C₄₇⋊#95	—	2	2	no	—
34	C₄₇⋊#95	C₂×C₄	1	4	yes	complemented
35	C₂²×D₄×C₄₇	—	2	1	no	—
36	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	—	2	1	no	—
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	#121×C₄₇	—	2	2	no	—
42	#121×C₄₇	C₂×C₄	1	4	yes	—
43	C₄×D₄×C₄₇	—	4	2	no	—
44	C₄×D₄×C₄₇	—	4	2	no	—
45	C₄×D₄×C₄₇	—	4	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
47	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄²×C₄₇	—	2	1	no	—
56	C₂×C₄²×C₄₇	—	4	2	no	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
61	#95×C₄₇	—	2	1	no	—
62	#95×C₄₇	—	2	1	no	—
63	#95×C₄₇	—	2	1	no	—
64	C₂⁴×C₄₇	—	2	1	no	—
65	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂×D₄×C₄₇	—	2	4	no	—
67	C₂×D₄×C₄₇	—	2	1	no	—
68	C₂×D₄×C₄₇	—	4	1	no	—
69	C₂×D₄×C₄₇	—	4	1	no	—
70	C₂×D₄×C₄₇	—	4	1	no	—
71	C₂×D₄×C₄₇	—	4	1	no	—
72	C₂×D₄×C₄₇	—	4	2	no	—
73	C₂×D₄×C₄₇	C₄²	1	2	yes	complemented
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	1	no	—
80	C₂²×C₄×C₄₇	—	2	1	no	—
81	C₂²×C₄×C₄₇	—	4	1	no	—
82	C₂²×C₄×C₄₇	—	4	1	no	—
83	C₂²×C₄×C₄₇	—	4	1	no	—
84	C₂²×C₄×C₄₇	—	4	2	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	—	4	2	no	—
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	D₈	1	2	yes	—
92	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	#41	1	2	yes	—
97	C₂²×Dic₄₇	—	2	4	no	—
98	C₂²×Dic₄₇	—	2	4	no	—
99	C₂²×Dic₄₇	—	2	4	no	—
100	C₂²×Dic₄₇	—	4	2	no	—
101	C₂²×Dic₄₇	—	4	2	no	—
102	C₂²×Dic₄₇	—	4	2	no	—
103	C₂²×Dic₄₇	—	4	2	no	—
104	C₄⋊C₄×C₄₇	—	2	1	no	—
105	C₄⋊C₄×C₄₇	—	4	1	no	—
106	C₄⋊C₄×C₄₇	—	4	1	no	—
107	C₄⋊C₄×C₄₇	—	4	2	no	—
108	C₄⋊C₄×C₄₇	C₄²	1	2	yes	complemented
109	C₂²⋊C₄×C₄₇	—	2	4	no	—
110	C₂²⋊C₄×C₄₇	—	4	2	no	—
111	C₂²⋊C₄×C₄₇	—	4	1	no	—
112	C₂²⋊C₄×C₄₇	—	4	1	no	—
113	C₂²⋊C₄×C₄₇	—	4	2	no	—
114	C₂²⋊C₄×C₄₇	—	4	2	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	4	1	no	—
118	C₄²×C₄₇	—	4	1	no	—
119	C₄²×C₄₇	—	4	2	no	—
120	C₄×Dic₄₇	—	4	8	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	4	2	no	—
123	C₂×C₄₇⋊C₈	—	4	2	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	—	2	1	no	—
127	C₂³×C₄₇	—	2	1	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	4	1	no	—
130	C₂³×C₄₇	—	4	1	no	—
131	C₂³×C₄₇	—	4	1	no	—
132	C₂³×C₄₇	—	4	1	no	—
133	C₂³×C₄₇	—	4	1	no	—
134	C₂³×C₄₇	—	4	1	no	—
135	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₄₇	C₄×D₄	1	2	yes	—
137	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
138	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
139	C₂³×C₄₇	#135	1	2	yes	—
140	D₄×C₄₇	—	4	2	no	—
141	D₄×C₄₇	—	4	2	no	—
142	D₄×C₄₇	—	4	4	no	—
143	D₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	8	4	no	—
170	C₂×C₄×C₄₇	#99	1	2	yes	—
171	C₂×C₄×C₄₇	#102	1	2	yes	—
172	C₂×C₄×C₄₇	#102	1	2	yes	—
173	C₂×C₄×C₄₇	#104	1	2	yes	—
174	C₂×C₄×C₄₇	#104	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×Dic₄₇	—	2	8	no	—
179	C₂×Dic₄₇	—	4	4	no	—
180	C₂×Dic₄₇	—	4	4	no	—
181	C₂×Dic₄₇	—	4	4	no	—
182	C₂×Dic₄₇	—	4	4	no	—
183	C₂×Dic₄₇	—	4	4	no	—
184	C₂×Dic₄₇	—	4	4	no	—
185	C₄₇⋊C₈	—	4	4	no	—
186	C₄×#327	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	—	8	1	no	—
199	C₂²×C₄₇	—	8	1	no	—
200	C₂²×C₄₇	—	8	1	no	—
201	C₂²×C₄₇	—	8	1	no	—
202	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×#99	1	1	yes	characteristic
204	C₂²×C₄₇	#410	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
206	C₂²×C₄₇	#416	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
209	C₂²×C₄₇	C₄×D₈	1	2	yes	—
210	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	—	2	1	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	4	1	no	—
217	C₄×C₄₇	—	4	2	no	—
218	C₄×C₄₇	—	8	1	no	—
219	C₄×C₄₇	—	8	1	no	—
220	C₄×C₄₇	#327	1	4	yes	complemented
221	Dic₄₇	—	4	8	no	—
222	C₄×#121	D₄₇	1	1	yes	characteristic
223	C₄×C₂²⋊C₈	—	47	1	no	—
224	C₂×#327	—	47	2	no	—
225	C₄×#95	—	47	1	no	—
226	#1294	—	47	2	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	2	2	no	—
229	C₂×C₄₇	—	8	2	no	—
230	C₂×C₄₇	C₂×#327	1	1	yes	characteristic
231	C₂×C₄₇	#1500	1	1	yes	characteristic
232	C₂×C₄₇	#1501	1	1	yes	characteristic
233	C₂×C₄₇	#1502	1	1	yes	characteristic
234	C₂×C₄₇	C₄×#99	1	1	yes	characteristic
235	C₂×C₄₇	C₄×#104	1	1	yes	characteristic
236	C₂×C₄₇	C₄×#102	1	1	yes	characteristic
237	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
238	C₂×C₄×D₄	—	2	1	no	—
239	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic, complemented
240	C₂²×C₄²	—	94	1	no	—
241	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	—	47	2	no	—
243	C₂×C₄×C₈	—	94	1	no	—
244	#390	Dic₄₇	1	1	yes	characteristic, complemented
245	#389	Dic₄₇	1	1	yes	characteristic, complemented
246	#388	—	2	1	no	—
247	#386	—	2	1	no	—
248	#380	C₂×D₄₇	1	1	yes	characteristic
249	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic, complemented
250	C₄×C₂²⋊C₄	—	2	1	no	—
251	C₂×#95	—	47	2	no	—
252	C₂×#95	—	94	1	no	—
253	#336	—	94	1	no	—
254	#327	—	47	8	no	—
255	C₄₇	C₄×#327	1	1	yes	characteristic, complemented, Sylow
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	—	94	2	no	—
260	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
261	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
262	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
263	C₂²×C₈	—	94	2	no	—
264	#121	—	2	2	no	—
265	#121	C₄×D₄₇	1	4	yes	—
266	C₄×D₄	—	4	2	no	—
267	C₄×D₄	—	4	2	no	—
268	C₄×D₄	—	4	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	4	2	no	—
280	C₂×C₄²	—	94	4	no	—
281	C₂×C₄²	—	188	2	no	—
282	C₂×C₄²	—	188	2	no	—
283	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
284	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
285	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
286	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂²⋊C₈	—	47	4	no	—
288	C₂²⋊C₈	—	94	2	no	—
289	C₄×C₈	—	188	2	no	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	47	4	no	—
294	#95	—	94	4	no	—
295	#95	—	94	2	no	—
296	C₂⁴	—	2	1	no	—
297	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	C₄×Dic₄₇	1	2	yes	complemented
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	94	4	no	—
320	C₂²×C₄	—	94	4	no	—
321	C₂²×C₄	—	94	4	no	—
322	C₂²×C₄	—	188	2	no	—
323	C₂²×C₄	—	188	2	no	—
324	C₂²×C₄	—	188	2	no	—
325	C₂²×C₄	—	188	2	no	—
326	C₂²×C₄	#10625334	1	2	yes	—
327	C₂²×C₄	#10625335	1	2	yes	—
328	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
333	C₂²×C₄	#10625350	1	2	yes	—
334	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
336	C₂×C₈	—	94	4	no	—
337	C₂×C₈	—	188	2	no	—
338	C₂×C₈	—	188	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	C₄×Dic₄₇	1	2	yes	complemented
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	1	no	—
353	C₄²	—	4	1	no	—
354	C₄²	—	4	2	no	—
355	C₄²	—	188	8	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
368	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
369	C₂³	C₂×#10625334	1	1	yes	characteristic
370	C₂³	C₂×#10625335	1	1	yes	characteristic
371	C₂³	#13094044	1	2	yes	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	4	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	—	94	8	no	—
403	C₂×C₄	—	188	4	no	—
404	C₂×C₄	—	188	4	no	—
405	C₂×C₄	—	188	4	no	—
406	C₂×C₄	—	188	4	no	—
407	C₂×C₄	—	188	4	no	—
408	C₂×C₄	—	188	4	no	—
409	C₂×C₄	#13093939	1	2	yes	—
410	C₂×C₄	#13093945	1	2	yes	—
411	C₂×C₄	#13093945	1	2	yes	—
412	C₂×C₄	#13093951	1	2	yes	—
413	C₂×C₄	#13093951	1	2	yes	—
414	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
415	C₂×C₄	#13093983	1	1	yes	characteristic
416	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
417	C₈	—	188	4	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
434	C₂²	C₂×#13093939	1	1	yes	characteristic
435	C₂²	#15689097	1	1	yes	characteristic
436	C₂²	C₂×#13093945	1	1	yes	characteristic
437	C₂²	#15689119	1	1	yes	characteristic
438	C₂²	C₂×#13093951	1	1	yes	characteristic
439	C₂²	C₂×#13093951	1	1	yes	characteristic
440	C₂²	C₄×#10625334	1	2	yes	—
441	C₂²	C₄×#10625335	1	2	yes	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	1	no	—
451	C₄	—	188	8	no	—
452	C₄	#15688857	1	4	yes	direct product factor
453	C₂	—	2	2	no	—
454	C₂	—	2	2	no	—
455	C₂	—	8	2	no	—
456	C₂	C₂×#15688857	1	1	yes	characteristic
457	C₂	#20241874	1	1	yes	characteristic
458	C₂	#20241879	1	1	yes	characteristic
459	C₂	#20241883	1	1	yes	characteristic
460	C₂	C₄×#13093939	1	1	yes	characteristic
461	C₂	C₄×#13093951	1	1	yes	characteristic
462	C₂	C₄×#13093945	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄×#121×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#121×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₄×#121	D₄₇
hypocenter	C₄₇	C₄×#327
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. C₄×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
3. C₄×C₄₇⋊#95	C₂	semidirect
4. #20241266	C₂	semidirect
12. #15688857	C₄	direct (N × H)
15. C₂×C₄×D₄×C₄₇	C₄	semidirect
17. C₄₇×#390	C₄	semidirect
18. C₄₇×#389	C₄	semidirect
22. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
30. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
34. C₄₇⋊#95	C₂×C₄	semidirect
73. C₂×D₄×C₄₇	C₄²	semidirect
108. C₄⋊C₄×C₄₇	C₄²	semidirect
220. C₄×C₄₇	#327	semidirect
239. C₂×C₄×D₄	Dic₄₇	semidirect
244. #390	Dic₄₇	semidirect
245. #389	Dic₄₇	semidirect
249. C₄×C₄⋊C₄	Dic₄₇	semidirect
255. C₄₇	C₄×#327	semidirect
305. C₂×D₄	C₄×Dic₄₇	semidirect
343. C₄⋊C₄	C₄×Dic₄₇	semidirect
452. C₄	#15688857	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₂×#15688857	2
C₄×C₄₇⋊#95	2
#20241266	2
C₄×#121×C₄₇	2
C₄×#327	47

Subgroups — C4×#15688857 #26107152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15688857 #26107152