Subgroups — C₄×#15689325 #26222459

Order 12032.

1104 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689325	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625336	C₂	1	2	yes	maximal
3	C₄²×D₁₈₈	C₂	1	1	yes	maximal, characteristic
4	#20244312	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244149	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244019	C₂	1	2	yes	maximal, complemented
7	#20243725	C₂	1	2	yes	maximal
8	#20243385	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093948	C₂	1	2	yes	maximal, complemented
11	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	2	yes	—
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₄₇	—	2	1	no	—
17	#15689325	C₄	1	8	yes	direct product factor
18	C₄×#10625336	—	2	8	no	—
19	C₂×#13093955	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×#13093948	C₂²	1	2	yes	—
24	C₂×#13093948	C₂²	1	2	yes	—
25	C₂×#13093944	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
31	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
32	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688878	C₂²	1	2	yes	—
36	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#391	C₂²	1	2	yes	—
39	C₄₇×#389	—	2	1	no	—
40	C₄₇×#389	—	2	1	no	—
41	C₄₇×#384	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
43	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
44	C₄³×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	—	2	1	no	—
47	C₂²×C₄×D₄₇	—	2	1	no	—
48	C₂²×C₄×D₄₇	—	2	1	no	—
49	C₂×#10625336	—	2	4	no	—
50	C₂×#10625336	—	2	4	no	—
51	C₂×#10625336	C₂×C₄	1	8	yes	—
52	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	C₄×D₁₈₈	—	2	2	no	—
55	C₄×D₁₈₈	—	2	2	no	—
56	C₄×D₁₈₈	—	2	2	no	—
57	C₄×D₁₈₈	—	2	2	no	—
58	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
59	C₄×D₁₈₈	D₄	1	4	yes	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
63	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
64	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
65	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	—	2	1	no	—
69	C₄²×D₄₇	—	4	4	no	—
70	#13093955	—	2	4	no	—
71	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
72	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
73	#13093948	—	2	4	no	—
74	#13093948	—	2	4	no	—
75	#13093948	C₂×C₄	1	8	yes	complemented
76	#13093944	—	2	4	no	—
77	C₄×C₄₇⋊C₈	—	2	4	no	—
78	C₄₇⋊#95	—	2	1	no	—
79	C₄₇⋊#95	—	2	1	no	—
80	C₄₇⋊#95	—	2	1	no	—
81	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₄₇	—	2	2	no	—
83	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
84	C₄×Q₈×C₄₇	—	2	4	no	—
85	C₄×Q₈×C₄₇	—	2	4	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₄₇	—	2	2	no	—
93	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	#95×C₄₇	—	2	2	no	—
101	#95×C₄₇	—	2	2	no	—
102	C₂³×D₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
118	C₂²×Dic₄₇	—	2	1	no	—
119	C₂²×Dic₄₇	—	2	1	no	—
120	C₂²×Dic₄₇	—	2	1	no	—
121	C₂×D₁₈₈	—	2	1	no	—
122	C₂×D₁₈₈	—	2	1	no	—
123	C₂×D₁₈₈	—	2	1	no	—
124	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
125	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
126	C₂×D₁₈₈	#41	1	2	yes	—
127	C₂×C₄×D₄₇	—	2	4	no	—
128	C₂×C₄×D₄₇	—	2	4	no	—
129	C₂×C₄×D₄₇	—	2	4	no	—
130	C₂×C₄×D₄₇	—	4	2	no	—
131	C₂×C₄×D₄₇	—	4	2	no	—
132	C₂×C₄×D₄₇	—	4	2	no	—
133	C₂×C₄×D₄₇	—	4	2	no	—
134	C₂×C₄×D₄₇	—	4	2	no	—
135	C₂×C₄×D₄₇	—	4	2	no	—
136	C₄⋊C₄×C₄₇	—	2	4	no	—
137	C₄⋊C₄×C₄₇	—	2	4	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	4	2	no	—
141	C₄⋊C₄×C₄₇	—	4	4	no	—
142	C₄⋊C₄×C₄₇	—	4	2	no	—
143	C₄²×C₄₇	—	2	2	no	—
144	C₄²×C₄₇	—	2	2	no	—
145	C₄²×C₄₇	—	2	1	no	—
146	C₄²×C₄₇	—	2	1	no	—
147	C₄²×C₄₇	—	4	1	no	—
148	C₄²×C₄₇	—	4	4	no	—
149	C₄²×C₄₇	SD₁₆	1	4	yes	complemented
150	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₇	C₂×D₄	1	2	yes	—
152	C₄²×C₄₇	#41	1	2	yes	—
153	C₄²×C₄₇	#41	1	2	yes	—
154	#10625336	—	2	16	no	—
155	(C₂×D₄₇)⋊C₄	—	2	4	no	—
156	(C₂×D₄₇)⋊C₄	—	2	4	no	—
157	(C₂×D₄₇)⋊C₄	—	2	4	no	—
158	C₄⋊Dic₄₇	—	2	1	no	—
159	C₄⋊Dic₄₇	—	2	1	no	—
160	C₄⋊Dic₄₇	—	2	1	no	—
161	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
162	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
163	C₄⋊Dic₄₇	#41	1	2	yes	—
164	C₄×Dic₄₇	—	4	2	no	—
165	C₄×Dic₄₇	—	4	2	no	—
166	C₄×Dic₄₇	—	4	2	no	—
167	C₂×C₄₇⋊C₈	—	2	2	no	—
168	C₂×C₄₇⋊C₈	—	2	2	no	—
169	C₂×C₄₇⋊C₈	—	2	2	no	—
170	C₂×C₄₇⋊C₈	—	2	2	no	—
171	C₂×C₄₇⋊C₈	—	2	2	no	—
172	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
173	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂²×D₄₇	—	2	2	no	—
175	C₂²×D₄₇	—	2	2	no	—
176	C₂²×D₄₇	—	2	2	no	—
177	C₂²×D₄₇	—	4	1	no	—
178	C₂²×D₄₇	—	4	1	no	—
179	C₂²×D₄₇	—	4	1	no	—
180	C₂²×D₄₇	—	4	1	no	—
181	Q₈×C₄₇	—	2	4	no	—
182	Q₈×C₄₇	—	2	4	no	—
183	Q₈×C₄₇	—	4	2	no	—
184	Q₈×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	1	no	—
188	C₂×C₄×C₄₇	—	2	1	no	—
189	C₂×C₄×C₄₇	—	2	1	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	4	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	2	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₄₇	#121	1	2	yes	—
203	C₂×C₄×C₄₇	#121	1	2	yes	—
204	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
205	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
206	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
207	C₂×C₄×C₄₇	#135	1	2	yes	—
208	C₂×C₄×C₄₇	#137	1	2	yes	—
209	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂×Dic₄₇	—	2	2	no	—
216	C₂×Dic₄₇	—	2	2	no	—
217	C₂×Dic₄₇	—	2	2	no	—
218	C₂×Dic₄₇	—	4	1	no	—
219	C₂×Dic₄₇	—	4	1	no	—
220	C₂×Dic₄₇	—	4	1	no	—
221	C₂×Dic₄₇	—	4	1	no	—
222	C₂×Dic₄₇	—	4	1	no	—
223	C₂×Dic₄₇	—	4	1	no	—
224	D₁₈₈	—	2	2	no	—
225	D₁₈₈	—	2	2	no	—
226	D₁₈₈	—	2	2	no	—
227	D₁₈₈	C₄×D₄	1	4	yes	—
228	C₄×D₄₇	—	4	8	no	—
229	C₄×D₄₇	—	4	8	no	—
230	C₄×D₄₇	—	4	8	no	—
231	C₄₇⋊C₈	—	2	4	no	—
232	C₄₇⋊C₈	—	4	2	no	—
233	C₄×#461	—	47	1	no	maximal, Sylow
234	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
236	C₂²×C₄₇	#525	1	1	yes	characteristic
237	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
238	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
239	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
240	C₂²×C₄₇	#575	1	1	yes	characteristic
241	C₂×D₄₇	—	2	4	no	—
242	C₂×D₄₇	—	4	2	no	—
243	C₂×D₄₇	—	4	2	no	—
244	C₂×D₄₇	—	4	2	no	—
245	C₂×D₄₇	—	4	2	no	—
246	C₂×D₄₇	—	4	2	no	—
247	C₂×D₄₇	—	4	2	no	—
248	C₄×C₄₇	—	2	2	no	—
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	—	2	2	no	—
251	C₄×C₄₇	—	4	1	no	—
252	C₄×C₄₇	—	4	4	no	—
253	C₄×C₄₇	—	8	2	no	—
254	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
255	C₄×C₄₇	#461	1	4	yes	complemented
256	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
258	C₄×C₄₇	#529	1	1	yes	characteristic
259	C₄×C₄₇	#532	1	1	yes	characteristic
260	Dic₄₇	—	4	2	no	—
261	Dic₄₇	—	4	2	no	—
262	Dic₄₇	—	4	2	no	—
263	C₂×#461	—	47	1	no	—
264	C₂×C₄×SD₁₆	—	47	2	no	—
265	C₄×C₄⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
266	C₄²×D₄	—	47	1	no	—
267	#1981	—	47	1	no	—
268	#1948	—	47	1	no	—
269	#1927	—	47	2	no	—
270	#1877	—	47	2	no	—
271	#1802	—	47	1	no	—
272	C₄×C₄⋊C₈	—	47	1	no	—
273	C₄×#103	—	47	2	no	—
274	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
275	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
276	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
277	C₂×C₄₇	C₂×#461	1	1	yes	characteristic
278	C₂×C₄₇	#3035	1	1	yes	characteristic
279	C₂×C₄₇	#3101	1	1	yes	characteristic
280	C₂×C₄₇	#3107	1	1	yes	characteristic
281	D₄₇	—	4	4	no	—
282	C₂²×SD₁₆	—	47	2	no	—
283	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
284	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
285	C₂×C₄×D₄	—	47	1	no	—
286	C₂×C₄×D₄	—	47	1	no	—
287	C₂×C₄×D₄	—	47	1	no	—
288	C₂²×C₄²	—	94	1	no	—
289	#461	—	47	8	no	—
290	C₄×SD₁₆	—	94	8	no	—
291	C₂×#106	—	47	2	no	—
292	C₂×C₄⋊C₈	—	47	1	no	—
293	C₂×C₄⋊C₈	—	47	1	no	—
294	C₂×#103	—	47	2	no	—
295	C₂×#103	—	47	2	no	—
296	C₂×#103	—	47	2	no	—
297	C₂×#102	—	47	2	no	—
298	C₂×C₄×C₈	—	47	2	no	—
299	#391	C₂×D₄₇	1	2	yes	—
300	#389	—	2	1	no	—
301	#389	—	2	1	no	—
302	#384	C₂×D₄₇	1	1	yes	characteristic
303	C₄×C₄⋊C₄	—	2	1	no	—
304	C₄×C₄⋊C₄	—	2	1	no	—
305	C₄×C₄⋊C₄	—	47	1	no	—
306	C₄×C₄⋊C₄	—	47	1	no	—
307	C₄×C₄⋊C₄	—	47	1	no	—
308	C₄×C₂²⋊C₄	—	94	1	no	—
309	C₄×C₂²⋊C₄	—	94	1	no	—
310	C₄×C₂²⋊C₄	—	94	1	no	—
311	C₄³	C₂×D₄₇	1	1	yes	characteristic
312	#340	—	47	2	no	—
313	#340	—	47	2	no	—
314	#336	—	47	2	no	—
315	C₄₇	C₄×#461	1	1	yes	characteristic, complemented, Sylow
316	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
317	C₂²×D₄	—	47	1	no	—
318	C₂³×C₄	—	94	1	no	—
319	C₂³×C₄	—	94	1	no	—
320	C₂³×C₄	—	94	1	no	—
321	C₂×SD₁₆	—	47	8	no	—
322	C₂×SD₁₆	—	94	4	no	—
323	C₂×SD₁₆	—	94	4	no	—
324	C₂²×C₈	—	47	2	no	—
325	C₂²×C₈	—	47	2	no	—
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	C₄×D₄₇	1	4	yes	complemented
328	C₄×Q₈	—	2	4	no	—
329	C₄×Q₈	—	2	4	no	—
330	C₄×D₄	—	47	4	no	—
331	C₄×D₄	—	47	4	no	—
332	C₄×D₄	—	94	2	no	—
333	C₄×D₄	—	94	2	no	—
334	C₄×D₄	—	94	2	no	—
335	C₄×D₄	—	94	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	47	1	no	—
342	C₂×C₄⋊C₄	—	47	1	no	—
343	C₂×C₄⋊C₄	—	47	1	no	—
344	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
345	C₂×C₂²⋊C₄	—	94	1	no	—
346	C₂×C₂²⋊C₄	—	94	1	no	—
347	C₂×C₂²⋊C₄	—	94	1	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	94	1	no	—
350	C₂×C₄²	—	94	1	no	—
351	C₂×C₄²	—	94	1	no	—
352	C₂×C₄²	—	188	4	no	—
353	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
355	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
358	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
359	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
360	#106	—	94	4	no	—
361	C₄⋊C₈	—	47	4	no	—
362	C₄⋊C₈	—	94	2	no	—
363	#103	—	47	8	no	—
364	#103	—	94	4	no	—
365	#103	—	94	4	no	—
366	#102	—	94	4	no	—
367	C₄×C₈	—	94	4	no	—
368	#95	—	2	2	no	—
369	#95	—	2	2	no	—
370	#95	—	94	1	no	—
371	#95	—	94	1	no	—
372	#95	—	94	1	no	—
373	C₂⁴	—	94	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
380	C₂×D₄	—	47	2	no	—
381	C₂×D₄	—	47	2	no	—
382	C₂×D₄	—	47	2	no	—
383	C₂×D₄	—	94	1	no	—
384	C₂×D₄	—	94	1	no	—
385	C₂×D₄	—	94	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	94	4	no	—
389	C₂²×C₄	—	94	1	no	—
390	C₂²×C₄	—	94	1	no	—
391	C₂²×C₄	—	94	1	no	—
392	C₂²×C₄	—	94	4	no	—
393	C₂²×C₄	—	94	4	no	—
394	C₂²×C₄	—	188	2	no	—
395	C₂²×C₄	—	188	2	no	—
396	C₂²×C₄	—	188	2	no	—
397	C₂²×C₄	—	188	2	no	—
398	C₂²×C₄	—	188	2	no	—
399	C₂²×C₄	—	188	2	no	—
400	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
407	SD₁₆	—	94	16	no	—
408	C₂×C₈	—	47	4	no	—
409	C₂×C₈	—	94	2	no	—
410	C₂×C₈	—	94	2	no	—
411	C₂×C₈	—	94	2	no	—
412	C₂×C₈	—	94	2	no	—
413	C₂×C₈	—	94	2	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	4	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	47	2	no	—
422	C₄⋊C₄	—	47	2	no	—
423	C₄⋊C₄	—	47	2	no	—
424	C₄⋊C₄	—	94	1	no	—
425	C₄⋊C₄	—	94	1	no	—
426	C₄⋊C₄	—	94	1	no	—
427	C₂²⋊C₄	—	94	4	no	—
428	C₂²⋊C₄	—	94	4	no	—
429	C₂²⋊C₄	—	94	4	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	4	1	no	—
435	C₄²	—	4	4	no	—
436	C₄²	—	188	2	no	—
437	C₄²	—	188	2	no	—
438	C₄²	—	188	2	no	—
439	C₄²	#10625336	1	4	yes	complemented
440	C₄²	C₂×C₄×D₄₇	1	2	yes	—
441	C₄²	#10625350	1	2	yes	—
442	C₄²	D₄×D₄₇	1	2	yes	—
443	C₄²	#10625352	1	2	yes	—
444	C₂³	—	94	2	no	—
445	C₂³	—	94	2	no	—
446	C₂³	—	94	2	no	—
447	C₂³	—	188	1	no	—
448	C₂³	—	188	1	no	—
449	C₂³	—	188	1	no	—
450	C₂³	—	188	1	no	—
451	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
452	Q₈	—	2	4	no	—
453	Q₈	—	2	4	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	4	2	no	—
456	D₄	—	47	4	no	—
457	D₄	—	94	2	no	—
458	D₄	—	94	2	no	—
459	D₄	—	94	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	94	2	no	—
476	C₂×C₄	—	94	2	no	—
477	C₂×C₄	—	94	2	no	—
478	C₂×C₄	—	188	8	no	—
479	C₂×C₄	—	188	1	no	—
480	C₂×C₄	—	188	1	no	—
481	C₂×C₄	—	188	1	no	—
482	C₂×C₄	—	188	1	no	—
483	C₂×C₄	—	188	1	no	—
484	C₂×C₄	—	188	1	no	—
485	C₂×C₄	—	188	8	no	—
486	C₂×C₄	—	188	8	no	—
487	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
488	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
489	C₂×C₄	#13093995	1	2	yes	—
490	C₂×C₄	#13093995	1	2	yes	—
491	C₂×C₄	C₂×#10625336	1	2	yes	—
492	C₂×C₄	C₂×#10625336	1	2	yes	—
493	C₂×C₄	C₂×#10625336	1	2	yes	—
494	C₂×C₄	#13094044	1	2	yes	—
495	C₂×C₄	#13094055	1	2	yes	—
496	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
497	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
498	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
499	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
500	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
501	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
502	C₈	—	94	4	no	—
503	C₈	—	188	2	no	—
504	C₂²	—	94	4	no	—
505	C₂²	—	188	2	no	—
506	C₂²	—	188	2	no	—
507	C₂²	—	188	2	no	—
508	C₂²	—	188	2	no	—
509	C₂²	—	188	2	no	—
510	C₂²	—	188	2	no	—
511	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
512	C₂²	C₂×#13093995	1	1	yes	characteristic
513	C₂²	#15689630	1	1	yes	characteristic
514	C₂²	C₂²×#10625336	1	1	yes	characteristic
515	C₂²	C₂×#13094044	1	1	yes	characteristic
516	C₂²	C₂×#13094055	1	1	yes	characteristic
517	C₂²	#15689921	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	4	no	—
523	C₄	—	8	2	no	—
524	C₄	—	188	2	no	—
525	C₄	—	188	2	no	—
526	C₄	—	188	2	no	—
527	C₄	C₄×#10625336	1	4	yes	complemented
528	C₄	#15689325	1	4	yes	direct product factor
529	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
530	C₄	C₄×#10625352	1	1	yes	characteristic
531	C₄	#15689655	1	1	yes	characteristic
532	C₄	#15689670	1	1	yes	characteristic
533	C₂	—	188	4	no	—
534	C₂	C₄×#13093995	1	1	yes	characteristic
535	C₂	C₂×C₄×#10625336	1	1	yes	characteristic
536	C₂	C₄×#13094055	1	1	yes	characteristic
537	C₂	C₂×#15689325	1	1	yes	characteristic
538	C₂	#20252837	1	1	yes	characteristic
539	C₂	#20253392	1	1	yes	characteristic
540	C₂	#20253453	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	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₄×#461
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
4. #20244312	C₂	semidirect
5. #20244149	C₂	semidirect
6. #20244019	C₂	semidirect
9. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
10. C₄×#13093948	C₂	semidirect
11. C₄×C₄⋊Q₈×C₄₇	C₂	semidirect
17. #15689325	C₄	direct (N × H)
72. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
75. #13093948	C₂×C₄	semidirect
83. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
149. C₄²×C₄₇	SD₁₆	semidirect
254. C₄×C₄₇	C₄×SD₁₆	semidirect
255. C₄×C₄₇	#461	semidirect
265. C₄×C₄⋊Q₈	D₄₇	semidirect
315. C₄₇	C₄×#461	semidirect
327. C₄⋊Q₈	C₄×D₄₇	semidirect
439. C₄²	#10625336	semidirect
527. C₄	C₄×#10625336	semidirect
528. C₄	#15689325	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×#15689325	2
C₂×C₄×#10625336	2
C₄²×D₁₈₈	2
#20244312	2
#20244149	2
#20244019	2
#20243725	2
#20243385	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×#13093948	2
C₄×C₄⋊Q₈×C₄₇	2
C₄×#461	47

Subgroups — C4×#15689325 #26222459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689325 #26222459