Subgroups — C₄×#15689415 #26223867

Order 12032.

880 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689415	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₉₄	C₂	1	1	yes	maximal, characteristic
3	#20244337	C₂	1	1	yes	maximal, characteristic
4	#20244144	C₂	1	1	yes	maximal, characteristic
5	#20243977	C₂	1	2	yes	maximal
6	#20243641	C₂	1	2	yes	maximal
7	#20243390	C₂	1	1	yes	maximal, characteristic
8	C₄×#13093957	C₂	1	2	yes	maximal
9	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093947	C₂	1	2	yes	maximal
11	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#15689415	C₄	1	8	yes	direct product factor
16	C₂×#13093957	C₂²	1	2	yes	—
17	C₂×#13093957	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093947	C₂²	1	2	yes	—
21	C₂×#13093947	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
23	C₄×Dic₄₇⋊C₄	—	2	1	no	—
24	C₄×Dic₄₇⋊C₄	—	2	1	no	—
25	C₄×Dic₄₇⋊C₄	—	2	1	no	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄²×Dic₄₇	—	2	1	no	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688878	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
37	C₄₇×#391	—	2	1	no	—
38	C₄₇×#389	—	2	1	no	—
39	C₄₇×#389	C₂²	1	2	yes	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
43	C₄³×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₄×Dic₉₄	—	2	2	no	—
48	C₄×Dic₉₄	—	2	2	no	—
49	C₄×Dic₉₄	—	2	2	no	—
50	C₄×Dic₉₄	—	2	2	no	—
51	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
52	C₄×Dic₉₄	Q₈	1	4	yes	complemented
53	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	—	2	1	no	—
57	C₂×Dic₄₇⋊C₄	—	2	1	no	—
58	C₂×Dic₄₇⋊C₄	—	2	1	no	—
59	C₂×C₄×Dic₄₇	—	2	1	no	—
60	C₂×C₄×Dic₄₇	—	2	1	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₂×C₄×Dic₄₇	—	2	1	no	—
63	C₂×C₄×Dic₄₇	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	#13093957	—	2	4	no	—
66	#13093957	C₂×C₄	1	8	yes	—
67	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
68	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
69	#13093947	—	2	4	no	—
70	#13093947	C₂×C₄	1	8	yes	—
71	C₄×C₄₇⋊C₈	—	2	4	no	—
72	C₄₇⋊#95	—	2	1	no	—
73	C₄₇⋊#95	—	2	1	no	—
74	C₄₇⋊#95	—	2	1	no	—
75	C₂²×Q₈×C₄₇	—	2	1	no	—
76	C₄⋊Q₈×C₄₇	—	2	2	no	—
77	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
78	C₄×Q₈×C₄₇	—	4	4	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	—	2	2	no	—
86	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	#95×C₄₇	—	2	2	no	—
94	#95×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	4	no	—
96	C₂×Q₈×C₄₇	—	4	2	no	—
97	C₂×Q₈×C₄₇	—	4	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₇	—	2	1	no	—
108	C₂²×Dic₄₇	—	2	1	no	—
109	C₂²×Dic₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	1	no	—
111	C₂×Dic₉₄	—	2	1	no	—
112	C₂×Dic₉₄	—	2	1	no	—
113	C₂×Dic₉₄	—	2	1	no	—
114	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
115	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
116	C₂×Dic₉₄	#41	1	2	yes	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	4	2	no	—
122	C₄⋊C₄×C₄₇	—	4	4	no	—
123	C₄⋊C₄×C₄₇	—	4	2	no	—
124	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	1	no	—
128	C₄²×C₄₇	—	2	1	no	—
129	C₄²×C₄₇	—	4	1	no	—
130	C₄²×C₄₇	—	4	4	no	—
131	C₄²×C₄₇	Q₁₆	1	4	yes	—
132	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
134	C₄²×C₄₇	#41	1	2	yes	—
135	C₄²×C₄₇	#41	1	2	yes	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄⋊Dic₄₇	—	2	1	no	—
138	C₄⋊Dic₄₇	—	2	1	no	—
139	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
140	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
141	C₄⋊Dic₄₇	#41	1	2	yes	—
142	Dic₄₇⋊C₄	—	2	4	no	—
143	Dic₄₇⋊C₄	—	2	4	no	—
144	Dic₄₇⋊C₄	—	2	4	no	—
145	C₄×Dic₄₇	—	2	4	no	—
146	C₄×Dic₄₇	—	2	4	no	—
147	C₄×Dic₄₇	—	2	4	no	—
148	C₄×Dic₄₇	—	4	2	no	—
149	C₄×Dic₄₇	—	4	2	no	—
150	C₄×Dic₄₇	—	4	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
157	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
179	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
181	C₂×C₄×C₄₇	#135	1	2	yes	—
182	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	—	4	1	no	—
196	C₂×Dic₄₇	—	4	1	no	—
197	C₂×Dic₄₇	—	4	1	no	—
198	C₂×Dic₄₇	—	4	1	no	—
199	C₂×Dic₄₇	—	4	1	no	—
200	C₂×Dic₄₇	—	4	1	no	—
201	Dic₉₄	—	2	2	no	—
202	Dic₉₄	—	2	2	no	—
203	Dic₉₄	—	2	2	no	—
204	Dic₉₄	C₄×Q₈	1	4	yes	complemented
205	C₄₇⋊C₈	—	2	4	no	—
206	C₄₇⋊C₈	—	4	2	no	—
207	C₄×#477	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₂²×C₄₇	#525	1	1	yes	characteristic
211	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂²×C₄₇	#575	1	1	yes	characteristic
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	2	2	no	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	4	1	no	—
219	C₄×C₄₇	—	4	4	no	—
220	C₄×C₄₇	—	8	2	no	—
221	C₄×C₄₇	C₄×Q₁₆	1	4	yes	—
222	C₄×C₄₇	#477	1	4	yes	complemented
223	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
224	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
225	C₄×C₄₇	#529	1	1	yes	characteristic
226	C₄×C₄₇	#533	1	1	yes	characteristic
227	Dic₄₇	—	2	4	no	—
228	Dic₄₇	—	4	2	no	—
229	Dic₄₇	—	4	2	no	—
230	Dic₄₇	—	4	2	no	—
231	C₂×#477	—	47	1	no	—
232	C₄×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
233	C₄²×Q₈	—	47	1	no	—
234	#1987	—	47	1	no	—
235	#1947	—	47	1	no	—
236	#1921	—	47	2	no	—
237	#1863	—	47	2	no	—
238	#1803	—	47	1	no	—
239	C₄×#107	—	47	2	no	—
240	C₄×C₄⋊C₈	—	47	1	no	—
241	C₄×#103	—	47	2	no	—
242	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
244	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×C₄₇	C₂×#477	1	1	yes	characteristic
246	C₂×C₄₇	#3076	1	1	yes	characteristic
247	C₂×C₄₇	#3104	1	1	yes	characteristic
248	C₂×C₄₇	#3106	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
250	C₂×C₄×Q₈	—	2	1	no	—
251	C₂×C₄×Q₈	—	47	1	no	—
252	C₂×C₄×Q₈	—	47	1	no	—
253	C₂×C₄×Q₈	—	47	1	no	—
254	#477	—	47	8	no	—
255	C₂×#107	—	47	2	no	—
256	C₂×#107	—	47	2	no	—
257	C₂×C₄⋊C₈	—	47	1	no	—
258	C₂×C₄⋊C₈	—	47	1	no	—
259	C₂×#103	—	47	2	no	—
260	C₂×#103	—	47	2	no	—
261	C₂×C₄×C₈	—	47	2	no	—
262	#391	—	2	1	no	—
263	#389	—	2	1	no	—
264	#389	C₂×D₄₇	1	2	yes	—
265	#384	C₂×D₄₇	1	1	yes	characteristic
266	C₄×C₄⋊C₄	—	2	1	no	—
267	C₄×C₄⋊C₄	—	47	1	no	—
268	C₄×C₄⋊C₄	—	47	1	no	—
269	C₄×C₄⋊C₄	—	47	1	no	—
270	C₄×C₄⋊C₄	—	94	1	no	—
271	C₄×C₄⋊C₄	—	94	1	no	—
272	C₄×C₄⋊C₄	—	94	1	no	—
273	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
274	C₄³	—	94	1	no	—
275	C₄³	C₂×D₄₇	1	1	yes	characteristic
276	#340	—	47	2	no	—
277	#340	—	47	2	no	—
278	#340	—	47	2	no	—
279	#340	—	47	2	no	—
280	#336	—	47	2	no	—
281	C₄₇	C₄×#477	1	1	yes	characteristic, complemented, Sylow
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	—	47	1	no	—
284	C₂²×C₈	—	47	2	no	—
285	C₂²×C₈	—	47	2	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	C₄×D₄₇	1	4	yes	—
288	C₄×Q₈	—	4	4	no	—
289	C₄×Q₈	—	47	4	no	—
290	C₄×Q₈	—	47	4	no	—
291	C₄×Q₈	—	94	2	no	—
292	C₄×Q₈	—	94	2	no	—
293	C₄×Q₈	—	94	2	no	—
294	C₄×Q₈	—	94	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	47	1	no	—
300	C₂×C₄⋊C₄	—	47	1	no	—
301	C₂×C₄⋊C₄	—	47	1	no	—
302	C₂×C₄⋊C₄	—	94	1	no	—
303	C₂×C₄⋊C₄	—	94	1	no	—
304	C₂×C₄⋊C₄	—	94	1	no	—
305	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	94	1	no	—
309	C₂×C₄²	—	94	1	no	—
310	C₂×C₄²	—	94	1	no	—
311	C₂×C₄²	—	94	1	no	—
312	C₂×C₄²	—	94	1	no	—
313	C₂×C₄²	—	94	1	no	—
314	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
315	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
316	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
317	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
318	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
319	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
320	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
321	#107	—	47	8	no	—
322	#107	—	94	4	no	—
323	C₄⋊C₈	—	47	4	no	—
324	C₄⋊C₈	—	94	2	no	—
325	#103	—	47	8	no	—
326	#103	—	94	4	no	—
327	C₄×C₈	—	94	4	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	94	1	no	—
331	#95	—	94	1	no	—
332	#95	—	94	1	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	47	2	no	—
337	C₂×Q₈	—	47	2	no	—
338	C₂×Q₈	—	47	2	no	—
339	C₂×Q₈	—	94	1	no	—
340	C₂×Q₈	—	94	1	no	—
341	C₂×Q₈	—	94	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	—	94	1	no	—
346	C₂²×C₄	—	94	1	no	—
347	C₂²×C₄	—	94	1	no	—
348	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
355	C₂×C₈	—	47	4	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	—	94	2	no	—
360	C₂×C₈	—	94	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	47	2	no	—
369	C₄⋊C₄	—	47	2	no	—
370	C₄⋊C₄	—	47	2	no	—
371	C₄⋊C₄	—	94	4	no	—
372	C₄⋊C₄	—	94	4	no	—
373	C₄⋊C₄	—	94	4	no	—
374	C₄⋊C₄	—	94	1	no	—
375	C₄⋊C₄	—	94	1	no	—
376	C₄⋊C₄	—	94	1	no	—
377	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	—	4	4	no	—
384	C₄²	—	94	4	no	—
385	C₄²	—	94	4	no	—
386	C₄²	—	94	4	no	—
387	C₄²	—	188	2	no	—
388	C₄²	—	188	2	no	—
389	C₄²	—	188	2	no	—
390	C₄²	#10625337	1	4	yes	—
391	C₄²	C₂×C₄×D₄₇	1	2	yes	—
392	C₄²	#10625350	1	2	yes	—
393	C₄²	Q₈×D₄₇	1	2	yes	—
394	C₄²	#10625354	1	2	yes	—
395	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
396	Q₈	—	4	8	no	—
397	Q₈	—	47	4	no	—
398	Q₈	—	94	2	no	—
399	Q₈	—	94	2	no	—
400	Q₈	—	94	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	94	2	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	94	2	no	—
419	C₂×C₄	—	94	2	no	—
420	C₂×C₄	—	94	2	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	—	188	1	no	—
423	C₂×C₄	—	188	1	no	—
424	C₂×C₄	—	188	1	no	—
425	C₂×C₄	—	188	1	no	—
426	C₂×C₄	—	188	1	no	—
427	C₂×C₄	—	188	1	no	—
428	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
429	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
430	C₂×C₄	#13094000	1	2	yes	—
431	C₂×C₄	#13094000	1	2	yes	—
432	C₂×C₄	C₂×#10625337	1	2	yes	—
433	C₂×C₄	C₂×#10625337	1	2	yes	—
434	C₂×C₄	C₂×#10625337	1	2	yes	—
435	C₂×C₄	#13094044	1	2	yes	—
436	C₂×C₄	#13094050	1	2	yes	—
437	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
438	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
439	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
440	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
441	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
442	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
443	C₈	—	94	4	no	—
444	C₈	—	188	2	no	—
445	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
446	C₂²	C₂×#13094000	1	1	yes	characteristic
447	C₂²	#15689630	1	1	yes	characteristic
448	C₂²	C₂²×#10625337	1	1	yes	characteristic
449	C₂²	C₂×#13094044	1	1	yes	characteristic
450	C₂²	C₂×#13094050	1	1	yes	characteristic
451	C₂²	#15689921	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	—	94	4	no	—
459	C₄	—	188	2	no	—
460	C₄	—	188	2	no	—
461	C₄	—	188	2	no	—
462	C₄	C₄×#10625337	1	4	yes	—
463	C₄	#15689415	1	4	yes	direct product factor
464	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
465	C₄	C₄×#10625354	1	1	yes	characteristic
466	C₄	#15689660	1	1	yes	characteristic
467	C₄	#15689677	1	1	yes	characteristic
468	C₂	C₄×#13094000	1	1	yes	characteristic
469	C₂	C₂×C₄×#10625337	1	1	yes	characteristic
470	C₂	C₄×#13094050	1	1	yes	characteristic
471	C₂	C₂×#15689415	1	1	yes	characteristic
472	C₂	#20253170	1	1	yes	characteristic
473	C₂	#20253423	1	1	yes	characteristic
474	C₂	#20253442	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₄⋊Q₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₄×#477
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
15. #15689415	C₄	direct (N × H)
52. C₄×Dic₉₄	Q₈	semidirect
204. Dic₉₄	C₄×Q₈	semidirect
222. C₄×C₄₇	#477	semidirect
281. C₄₇	C₄×#477	semidirect
463. C₄	#15689415	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×#15689415	2
C₄²×Dic₉₄	2
#20244337	2
#20244144	2
#20243977	2
#20243641	2
#20243390	2
C₄×#13093957	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×#13093947	2
C₄×C₄⋊Q₈×C₄₇	2
C₄×#477	47

Subgroups — C4×#15689415 #26223867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689415 #26223867