Subgroups — #26217825

Order 12032.

1708 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689890	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689140	C₂	1	2	yes	maximal, complemented
3	C₂×#15689097	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243772	C₂	1	8	yes	maximal, complemented
5	#20243098	C₂	1	2	yes	maximal, complemented
6	C₄₇×#3449	C₂	1	1	yes	maximal, characteristic
7	#15689890	—	2	4	no	—
8	#15689890	—	2	2	no	—
9	#15689890	C₂²	1	4	yes	complemented
10	C₂×#13094031	—	2	4	no	—
11	C₂²×#10625329	—	2	2	no	—
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂×#13093983	C₂²	1	2	yes	—
14	#15689140	—	2	4	no	—
15	#15689140	C₂²	1	8	yes	complemented
16	C₂×#13093951	—	2	4	no	—
17	#15689097	—	2	2	no	—
18	#15689097	C₂²	1	4	yes	complemented
19	C₂×#13093939	—	2	2	no	—
20	#15688883	C₂²	1	8	yes	complemented
21	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#537	—	2	2	no	—
24	C₄₇×#536	C₄	1	2	yes	complemented
25	C₄₇×#536	C₄	1	2	yes	complemented
26	C₄₇×#535	C₄	1	2	yes	complemented
27	C₄₇×#535	C₄	1	2	yes	complemented
28	C₄₇×#534	—	2	2	no	—
29	C₄₇×#532	C₂²	1	4	yes	—
30	C₄₇×#525	—	2	2	no	—
31	C₄₇×#525	—	2	2	no	—
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	#13094031	—	2	16	no	—
34	#13094031	—	2	16	no	—
35	C₂×#10625329	—	2	4	no	—
36	C₂×#10625329	—	2	8	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	8	no	—
39	C₂×#10625329	—	2	2	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	D₄	1	4	yes	complemented
42	C₂×#10625329	D₄	1	4	yes	complemented
43	C₂×#10625329	C₂³	1	4	yes	—
44	C₂²×C₄₇⋊C₈	—	2	4	no	—
45	C₂²×C₄₇⋊C₈	—	2	2	no	—
46	#13093983	—	2	2	no	—
47	#13093983	—	2	2	no	—
48	#13093983	—	2	2	no	—
49	#13093983	C₂³	1	4	yes	—
50	C₂×C₄⋊Dic₄₇	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	#13093951	—	2	16	no	—
54	#13093939	—	2	8	no	—
55	C₂×#41×C₄₇	—	2	2	no	—
56	C₂×#41×C₄₇	—	2	2	no	—
57	C₂×#41×C₄₇	—	2	1	no	—
58	C₂×#41×C₄₇	—	2	1	no	—
59	C₂×#41×C₄₇	—	2	2	no	—
60	C₂×#41×C₄₇	—	2	2	no	—
61	C₂×#41×C₄₇	—	2	2	no	—
62	C₂×#41×C₄₇	—	2	2	no	—
63	C₂×#41×C₄₇	—	2	2	no	—
64	C₂×#41×C₄₇	—	2	2	no	—
65	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×#41×C₄₇	D₄	1	2	yes	—
68	C₂×#41×C₄₇	D₄	1	2	yes	—
69	C₂×#41×C₄₇	C₂³	1	2	yes	—
70	C₂×#41×C₄₇	C₂³	1	2	yes	—
71	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₄×C₄₇	—	2	1	no	—
74	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂²×D₄×C₄₇	D₄	1	2	yes	—
77	C₂³×C₄×C₄₇	—	2	1	no	—
78	C₂³×C₄×C₄₇	D₄	1	2	yes	—
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
81	#127×C₄₇	C₂×C₄	1	4	yes	complemented
82	#124×C₄₇	C₂×C₄	1	4	yes	complemented
83	#124×C₄₇	C₂×C₄	1	4	yes	complemented
84	#123×C₄₇	—	2	4	no	—
85	#123×C₄₇	—	2	4	no	—
86	C₂²⋊Q₈×C₄₇	—	2	4	no	—
87	C₂²⋊Q₈×C₄₇	—	2	4	no	—
88	#121×C₄₇	—	2	4	no	—
89	#121×C₄₇	—	2	8	no	—
90	#121×C₄₇	—	2	4	no	—
91	#120×C₄₇	—	2	4	no	—
92	#120×C₄₇	—	2	4	no	—
93	C₄×D₄×C₄₇	—	2	8	no	—
94	#117×C₄₇	—	2	1	no	—
95	#117×C₄₇	—	2	1	no	—
96	#117×C₄₇	C₂×C₄	1	2	yes	—
97	#117×C₄₇	C₂×C₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
101	C₂⁴×C₄₇	—	2	1	no	—
102	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
103	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
104	#41×C₄₇	—	2	4	no	—
105	#41×C₄₇	—	2	4	no	—
106	#41×C₄₇	—	2	4	no	—
107	#41×C₄₇	—	2	4	no	—
108	#41×C₄₇	—	2	4	no	—
109	#41×C₄₇	—	2	4	no	—
110	#41×C₄₇	—	2	4	no	—
111	#41×C₄₇	—	2	4	no	—
112	#41×C₄₇	—	2	4	no	—
113	#41×C₄₇	—	2	4	no	—
114	#41×C₄₇	—	2	4	no	—
115	#41×C₄₇	—	2	4	no	—
116	#41×C₄₇	—	4	1	no	—
117	#41×C₄₇	—	4	1	no	—
118	#41×C₄₇	—	4	2	no	—
119	#41×C₄₇	—	4	2	no	—
120	#41×C₄₇	—	4	1	no	—
121	#41×C₄₇	—	4	1	no	—
122	C₂×Q₈×C₄₇	—	2	1	no	—
123	C₂×Q₈×C₄₇	—	2	2	no	—
124	C₂×Q₈×C₄₇	—	2	2	no	—
125	C₂×Q₈×C₄₇	—	2	2	no	—
126	C₂×Q₈×C₄₇	—	2	2	no	—
127	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
128	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₄₇	—	2	4	no	—
131	C₂×D₄×C₄₇	—	2	4	no	—
132	C₂×D₄×C₄₇	—	2	2	no	—
133	C₂×D₄×C₄₇	—	2	2	no	—
134	C₂×D₄×C₄₇	—	2	8	no	—
135	C₂×D₄×C₄₇	—	2	1	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	4	2	no	—
141	C₂×D₄×C₄₇	—	4	2	no	—
142	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
143	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
144	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	2	no	—
149	C₂²×C₄×C₄₇	—	2	2	no	—
150	C₂²×C₄×C₄₇	—	2	2	no	—
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	2	2	no	—
155	C₂²×C₄×C₄₇	—	4	2	no	—
156	C₂²×C₄×C₄₇	—	4	2	no	—
157	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
158	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
159	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₄₇	#41	1	2	yes	—
168	C₂²×C₄×C₄₇	#41	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂²×Dic₄₇	—	4	2	no	—
171	C₄⋊C₄×C₄₇	—	2	2	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	—	2	8	no	—
174	C₂²⋊C₄×C₄₇	—	2	2	no	—
175	C₂²⋊C₄×C₄₇	—	2	2	no	—
176	C₂²⋊C₄×C₄₇	—	2	8	no	—
177	C₂²⋊C₄×C₄₇	—	2	8	no	—
178	C₄²×C₄₇	—	2	2	no	—
179	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
180	C₂²⋊Dic₄₇	—	2	4	no	—
181	C₂²⋊Dic₄₇	—	4	2	no	—
182	C₄⋊Dic₄₇	—	2	4	no	—
183	C₄⋊Dic₄₇	—	4	2	no	—
184	C₄×Dic₄₇	—	2	4	no	—
185	C₄×Dic₄₇	—	4	2	no	—
186	#10625329	—	2	16	no	—
187	#10625329	—	2	4	no	—
188	#10625329	—	2	4	no	—
189	#10625329	—	2	4	no	—
190	#10625329	C₂×D₄	1	8	yes	—
191	C₂×C₄₇⋊C₈	—	2	16	no	—
192	C₂×C₄₇⋊C₈	—	2	4	no	—
193	C₂×C₄₇⋊C₈	—	2	4	no	—
194	C₂×C₄₇⋊C₈	—	2	4	no	—
195	C₂³×C₄₇	—	2	2	no	—
196	C₂³×C₄₇	—	2	2	no	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	4	2	no	—
199	C₂³×C₄₇	—	8	1	no	—
200	C₂³×C₄₇	—	8	2	no	—
201	C₂³×C₄₇	—	8	2	no	—
202	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
203	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₄₇	#121	1	2	yes	—
206	C₂³×C₄₇	#121	1	2	yes	—
207	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₄₇	—	2	4	no	—
209	Q₈×C₄₇	—	2	4	no	—
210	Q₈×C₄₇	—	2	4	no	—
211	Q₈×C₄₇	—	4	1	no	—
212	Q₈×C₄₇	—	4	1	no	—
213	D₄×C₄₇	—	2	8	no	—
214	D₄×C₄₇	—	2	8	no	—
215	D₄×C₄₇	—	2	4	no	—
216	D₄×C₄₇	—	2	4	no	—
217	D₄×C₄₇	—	2	4	no	—
218	D₄×C₄₇	—	4	4	no	—
219	D₄×C₄₇	—	4	2	no	—
220	D₄×C₄₇	—	4	2	no	—
221	D₄×C₄₇	—	4	1	no	—
222	D₄×C₄₇	—	4	1	no	—
223	D₄×C₄₇	—	8	8	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	4	no	—
227	C₂×C₄×C₄₇	—	2	4	no	—
228	C₂×C₄×C₄₇	—	2	4	no	—
229	C₂×C₄×C₄₇	—	2	4	no	—
230	C₂×C₄×C₄₇	—	2	4	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	4	2	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	—	4	4	no	—
236	C₂×C₄×C₄₇	—	8	2	no	—
237	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
238	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
241	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#120	1	2	yes	—
246	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#121	1	2	yes	—
248	C₂×C₄×C₄₇	#121	1	2	yes	—
249	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
250	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
251	C₂×C₄×C₄₇	#123	1	2	yes	—
252	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
256	C₂×Dic₄₇	—	4	4	no	—
257	C₂×Dic₄₇	—	8	4	no	—
258	C₄₇⋊C₈	—	2	8	no	—
259	#20947	—	47	1	no	maximal, Sylow
260	C₂²×C₄₇	—	2	4	no	—
261	C₂²×C₄₇	—	4	2	no	—
262	C₂²×C₄₇	—	4	1	no	—
263	C₂²×C₄₇	—	4	1	no	—
264	C₂²×C₄₇	—	4	1	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	4	4	no	—
267	C₂²×C₄₇	—	4	4	no	—
268	C₂²×C₄₇	—	4	4	no	—
269	C₂²×C₄₇	—	4	2	no	—
270	C₂²×C₄₇	—	8	2	no	—
271	C₂²×C₄₇	—	8	4	no	—
272	C₂²×C₄₇	#386	1	1	yes	characteristic
273	C₂²×C₄₇	#386	1	1	yes	characteristic
274	C₂²×C₄₇	#386	1	2	yes	—
275	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₄₇	C₂×#121	1	2	yes	—
277	C₄×C₄₇	—	2	4	no	—
278	C₄×C₄₇	—	4	4	no	—
279	C₄×C₄₇	—	4	2	no	—
280	C₄×C₄₇	#386	1	1	yes	characteristic
281	C₄×C₄₇	#386	1	1	yes	characteristic
282	C₄×C₄₇	#386	1	2	yes	—
283	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
284	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
285	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
286	Dic₄₇	—	8	4	no	—
287	C₂×#568	—	47	1	no	—
288	#3449	D₄₇	1	1	yes	characteristic
289	C₂×#421	—	47	2	no	—
290	C₂×#410	—	47	1	no	—
291	#1884	—	47	8	no	—
292	#1733	—	47	2	no	—
293	C₂×C₄₇	—	2	2	no	—
294	C₂×C₄₇	—	2	1	no	—
295	C₂×C₄₇	—	2	1	no	—
296	C₂×C₄₇	—	2	1	no	—
297	C₂×C₄₇	—	2	2	no	—
298	C₂×C₄₇	—	4	4	no	—
299	C₂×C₄₇	—	8	2	no	—
300	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
301	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
302	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
303	#568	—	47	4	no	—
304	#568	—	94	4	no	—
305	#568	—	94	2	no	—
306	C₂×#131	—	94	4	no	—
307	C₂²×M₁₆	—	47	2	no	—
308	C₂²×M₁₆	—	94	2	no	—
309	#537	—	2	2	no	—
310	#536	Dic₄₇	1	2	yes	complemented
311	#536	Dic₄₇	1	2	yes	complemented
312	#535	Dic₄₇	1	2	yes	complemented
313	#535	Dic₄₇	1	2	yes	complemented
314	#534	—	2	2	no	—
315	#532	C₂×D₄₇	1	4	yes	—
316	#525	—	2	2	no	—
317	#525	—	2	2	no	—
318	C₂×#117	—	47	2	no	—
319	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
320	#421	—	47	8	no	—
321	#421	—	94	4	no	—
322	C₂×#104	—	94	4	no	—
323	#410	—	47	4	no	—
324	#410	—	94	2	no	—
325	C₂×#99	—	94	2	no	—
326	#339	—	47	8	no	—
327	C₄₇	#20947	1	1	yes	characteristic, complemented, Sylow
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	C₂×Dic₄₇	1	2	yes	—
339	C₂×#41	C₂×Dic₄₇	1	2	yes	—
340	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
341	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
342	C₂×#41	C₂²×D₄₇	1	2	yes	—
343	C₂×#41	C₂²×D₄₇	1	2	yes	—
344	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
345	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
348	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
349	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
352	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
353	#131	—	94	16	no	—
354	#131	—	94	16	no	—
355	C₂×M₁₆	—	47	4	no	—
356	C₂×M₁₆	—	47	4	no	—
357	C₂×M₁₆	—	47	4	no	—
358	C₂×M₁₆	—	94	4	no	—
359	C₂×M₁₆	—	94	8	no	—
360	C₂×M₁₆	—	94	2	no	—
361	C₂×M₁₆	—	94	2	no	—
362	C₂×M₁₆	—	94	2	no	—
363	C₂×M₁₆	—	94	8	no	—
364	C₂²×C₈	—	94	4	no	—
365	C₂²×C₈	—	94	2	no	—
366	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
367	#127	C₂×Dic₄₇	1	4	yes	complemented
368	#124	C₂×Dic₄₇	1	4	yes	complemented
369	#124	C₂×Dic₄₇	1	4	yes	complemented
370	#123	—	2	4	no	—
371	#123	—	2	4	no	—
372	C₂²⋊Q₈	—	2	4	no	—
373	C₂²⋊Q₈	—	2	4	no	—
374	#121	—	2	4	no	—
375	#121	—	2	8	no	—
376	#121	—	2	4	no	—
377	#120	—	2	4	no	—
378	#120	—	2	4	no	—
379	C₄×D₄	—	2	8	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	47	4	no	—
383	#117	—	94	2	no	—
384	#117	—	94	2	no	—
385	#117	—	94	2	no	—
386	#117	C₂×Dic₄₇	1	2	yes	—
387	#117	C₂×Dic₄₇	1	2	yes	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	94	2	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	94	2	no	—
392	C₂×C₄²	—	94	2	no	—
393	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
394	#104	—	94	16	no	—
395	#99	—	94	8	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
398	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
399	#41	—	2	4	no	—
400	#41	—	2	4	no	—
401	#41	—	2	4	no	—
402	#41	—	2	4	no	—
403	#41	—	2	4	no	—
404	#41	—	2	4	no	—
405	#41	—	2	4	no	—
406	#41	—	2	4	no	—
407	#41	—	2	4	no	—
408	#41	—	2	4	no	—
409	#41	—	2	4	no	—
410	#41	—	2	4	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	—	4	2	no	—
414	#41	—	4	2	no	—
415	#41	—	4	1	no	—
416	#41	—	4	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
423	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
424	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
438	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
439	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
440	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
441	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	188	2	no	—
453	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
454	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
455	C₂²×C₄	D₄×D₄₇	1	2	yes	—
456	C₂²×C₄	D₄×D₄₇	1	2	yes	—
457	C₂²×C₄	#10625352	1	2	yes	—
458	C₂²×C₄	#10625352	1	2	yes	—
459	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
462	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
466	M₁₆	—	47	8	no	—
467	M₁₆	—	94	16	no	—
468	M₁₆	—	94	4	no	—
469	M₁₆	—	94	4	no	—
470	M₁₆	—	94	4	no	—
471	C₂×C₈	—	94	16	no	—
472	C₂×C₈	—	94	4	no	—
473	C₂×C₈	—	94	4	no	—
474	C₂×C₈	—	94	4	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	94	4	no	—
479	C₄⋊C₄	—	188	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	94	4	no	—
485	C₂²⋊C₄	—	188	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	94	4	no	—
488	C₄²	—	188	2	no	—
489	C₄²	C₂²×Dic₄₇	1	4	yes	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	8	1	no	—
495	C₂³	—	8	2	no	—
496	C₂³	—	8	2	no	—
497	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
498	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
499	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
500	C₂³	#13093996	1	2	yes	—
501	C₂³	#13093996	1	2	yes	—
502	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
503	Q₈	—	2	4	no	—
504	Q₈	—	2	4	no	—
505	Q₈	—	2	4	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	D₄	—	2	8	no	—
509	D₄	—	2	8	no	—
510	D₄	—	2	4	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	4	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	8	8	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	376	4	no	—
533	C₂×C₄	—	188	4	no	—
534	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
535	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
536	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
537	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
538	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
539	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
540	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
541	C₂×C₄	#13093992	1	1	yes	characteristic
542	C₂×C₄	#13093992	1	2	yes	—
543	C₂×C₄	#13093992	1	1	yes	characteristic
544	C₂×C₄	#13093996	1	2	yes	—
545	C₂×C₄	#13093996	1	2	yes	—
546	C₂×C₄	#13094005	1	1	yes	characteristic
547	C₂×C₄	#13094005	1	1	yes	characteristic
548	C₂×C₄	#13094005	1	2	yes	—
549	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
550	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
551	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂×#10625352	1	2	yes	—
553	C₈	—	94	8	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	4	no	—
566	C₂²	#15689003	1	1	yes	characteristic
567	C₂²	#15689003	1	1	yes	characteristic
568	C₂²	#15689003	1	2	yes	—
569	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
570	C₂²	C₂×#13093996	1	2	yes	—
571	C₄	—	2	4	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	2	no	—
574	C₄	—	376	4	no	—
575	C₄	#15689003	1	1	yes	characteristic
576	C₄	#15689003	1	1	yes	characteristic
577	C₄	#15689003	1	2	yes	—
578	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
579	C₄	C₂×#13093992	1	1	yes	characteristic
580	C₄	C₂×#13094005	1	1	yes	characteristic
581	C₂	—	2	1	no	—
582	C₂	—	2	2	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	2	no	—
586	C₂	—	4	4	no	—
587	C₂	—	8	2	no	—
588	C₂	C₂×#15689003	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13093992
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3449	C₂
socle	C₂×C₄₇	C₂×#386
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3449	D₄₇
hypocenter	C₄₇	#20947
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #3449

Complements

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

N	H ≅ G/N	type
1. C₂×#15689890	C₂	semidirect
2. C₂×#15689140	C₂	semidirect
3. C₂×#15689097	C₂	semidirect
4. #20243772	C₂	semidirect
5. #20243098	C₂	semidirect
9. #15689890	C₂²	semidirect
15. #15689140	C₂²	semidirect
18. #15689097	C₂²	semidirect
20. #15688883	C₂²	semidirect
24. C₄₇×#536	C₄	semidirect
25. C₄₇×#536	C₄	semidirect
26. C₄₇×#535	C₄	semidirect
27. C₄₇×#535	C₄	semidirect
41. C₂×#10625329	D₄	semidirect
42. C₂×#10625329	D₄	semidirect
80. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
81. #127×C₄₇	C₂×C₄	semidirect
82. #124×C₄₇	C₂×C₄	semidirect
83. #124×C₄₇	C₂×C₄	semidirect
310. #536	Dic₄₇	semidirect
311. #536	Dic₄₇	semidirect
312. #535	Dic₄₇	semidirect
313. #535	Dic₄₇	semidirect
327. C₄₇	#20947	semidirect
366. C₄⋊Q₈	C₂×Dic₄₇	semidirect
367. #127	C₂×Dic₄₇	semidirect
368. #124	C₂×Dic₄₇	semidirect
369. #124	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689890	2
C₂×#15689140	2
C₂×#15689097	2
#20243772	2
#20243098	2
C₄₇×#3449	2
#20947	47