Subgroups — #26227680

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252083	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689090	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244277	C₂	1	2	yes	maximal, complemented
4	#20244094	C₂	1	2	yes	maximal, complemented
5	#20244038	C₂	1	2	yes	maximal, complemented
6	#20243717	C₂	1	2	yes	maximal, complemented
7	#20243691	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243595	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243332	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3002	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	1	yes	characteristic, complemented
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#15689195	—	2	1	no	—
16	#15689195	—	2	1	no	—
17	D₄×C₄₇⋊C₈	—	2	1	no	—
18	D₄×C₄₇⋊C₈	—	2	1	no	—
19	C₂×#13093960	C₂²	1	2	yes	complemented
20	#15689150	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13093951	C₂²	1	2	yes	—
22	C₂×#13093951	C₂²	1	2	yes	—
23	C₂×#13093951	C₂²	1	2	yes	complemented
24	#15689090	—	2	1	no	—
25	#15689090	—	2	1	no	—
26	#15689090	C₂²	1	2	yes	—
27	#15689090	C₂²	1	2	yes	—
28	#15689090	C₂²	1	1	yes	characteristic, complemented
29	#15689087	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
31	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
32	#15689079	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
34	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688888	C₂²	1	2	yes	complemented
36	#15688882	C₂²	1	2	yes	complemented
37	#15688877	C₂²	1	2	yes	complemented
38	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#135×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#525	C₂²	1	1	yes	characteristic
41	C₄₇×#452	C₄	1	2	yes	complemented
42	C₄₇×#451	C₄	1	1	yes	characteristic, complemented
43	C₄₇×#450	C₄	1	1	yes	characteristic, complemented
44	C₄₇×#449	C₄	1	2	yes	complemented
45	C₄₇×#448	C₄	1	1	yes	characteristic, complemented
46	C₄₇×#447	C₄	1	1	yes	characteristic, complemented
47	C₄₇×#416	C₂²	1	2	yes	—
48	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
49	#13094031	—	4	2	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	4	2	no	—
53	C₂×#10625329	C₂³	1	1	yes	characteristic
54	C₂×#10625329	C₂³	1	1	yes	characteristic
55	C₂×#10625329	C₂³	1	2	yes	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	4	2	no	—
59	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
60	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
63	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
67	#13093960	—	4	2	no	—
68	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
69	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
70	#13093951	—	4	2	no	—
71	#13093951	—	4	2	no	—
72	#13093951	—	4	2	no	—
73	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
75	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
81	#13093935	—	2	1	no	—
82	C₄×C₄₇⋊C₈	—	2	1	no	—
83	C₈×Dic₄₇	—	4	2	no	—
84	C₄₇⋊#95	—	2	1	no	—
85	C₂×#41×C₄₇	—	2	1	no	—
86	C₂×#41×C₄₇	—	2	1	no	—
87	C₂×#41×C₄₇	—	4	2	no	—
88	C₂×#41×C₄₇	—	4	2	no	—
89	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
90	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×#41×C₄₇	C₂³	1	2	yes	—
92	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂²×D₄×C₄₇	—	2	1	no	—
94	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂³×C₄×C₄₇	—	2	1	no	—
96	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
97	#135×C₄₇	—	4	2	no	—
98	#135×C₄₇	—	4	2	no	—
99	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
100	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
101	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
102	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
103	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
104	#123×C₄₇	—	2	1	no	—
105	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
107	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
108	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
109	#120×C₄₇	—	2	1	no	—
110	C₄×D₄×C₄₇	—	2	1	no	—
111	C₄×D₄×C₄₇	—	2	1	no	—
112	#117×C₄₇	C₂³	1	1	yes	characteristic
113	#103×C₄₇	C₂×C₄	1	2	yes	—
114	#103×C₄₇	C₂×C₄	1	2	yes	—
115	#102×C₄₇	C₂×C₄	1	2	yes	—
116	#102×C₄₇	C₂×C₄	1	2	yes	—
117	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
118	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂⁴×C₄₇	—	2	1	no	—
121	C₂⁴×C₄₇	#41	1	1	yes	characteristic
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	2	no	—
124	#41×C₄₇	—	2	2	no	—
125	#41×C₄₇	—	2	2	no	—
126	#41×C₄₇	—	2	2	no	—
127	#41×C₄₇	—	2	2	no	—
128	#41×C₄₇	—	4	2	no	—
129	#41×C₄₇	—	4	2	no	—
130	#41×C₄₇	—	4	4	no	—
131	#41×C₄₇	—	4	2	no	—
132	#41×C₄₇	—	4	2	no	—
133	C₂×Q₈×C₄₇	—	2	1	no	—
134	C₂×Q₈×C₄₇	—	4	2	no	—
135	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×D₄×C₄₇	—	2	1	no	—
138	C₂×D₄×C₄₇	—	2	1	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	1	no	—
141	C₂×D₄×C₄₇	—	2	2	no	—
142	C₂×D₄×C₄₇	—	2	1	no	—
143	C₂×D₄×C₄₇	—	4	2	no	—
144	C₂×D₄×C₄₇	—	4	4	no	—
145	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	2	no	—
149	C₂²×C₄×C₄₇	—	2	1	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	—	4	2	no	—
154	C₂²×C₄×C₄₇	—	4	2	no	—
155	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
161	C₂²×Dic₄₇	—	2	2	no	—
162	Q₁₆×C₄₇	—	4	2	no	—
163	SD₁₆×C₄₇	—	4	2	no	—
164	SD₁₆×C₄₇	—	4	2	no	—
165	D₈×C₄₇	—	4	2	no	—
166	C₂×C₈×C₄₇	—	2	2	no	—
167	C₂×C₈×C₄₇	—	2	2	no	—
168	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
170	C₄⋊C₄×C₄₇	—	2	1	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²⋊C₄×C₄₇	—	2	1	no	—
175	C₂²⋊C₄×C₄₇	—	2	1	no	—
176	C₂²⋊C₄×C₄₇	—	2	1	no	—
177	C₂²⋊C₄×C₄₇	—	2	1	no	—
178	C₂²⋊C₄×C₄₇	—	2	1	no	—
179	C₄²×C₄₇	—	2	1	no	—
180	C₂²⋊Dic₄₇	—	2	4	no	—
181	C₄×Dic₄₇	—	2	2	no	—
182	C₄×Dic₄₇	—	2	2	no	—
183	#10625329	—	2	2	no	—
184	#10625329	—	2	2	no	—
185	#10625329	—	2	2	no	—
186	#10625329	—	2	2	no	—
187	#10625329	—	4	2	no	—
188	#10625329	—	4	2	no	—
189	C₂×C₄₇⋊C₈	—	2	2	no	—
190	C₂×C₄₇⋊C₈	—	2	2	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	2	no	—
193	C₂×C₄₇⋊C₈	—	2	1	no	—
194	C₂×C₄₇⋊C₈	—	4	1	no	—
195	C₂×C₄₇⋊C₈	—	4	1	no	—
196	C₂×C₄₇⋊C₈	—	4	1	no	—
197	C₂×C₄₇⋊C₈	—	4	1	no	—
198	C₂×C₄₇⋊C₈	—	4	2	no	—
199	C₂×C₄₇⋊C₈	—	4	2	no	—
200	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
201	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
202	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
203	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	2	1	no	—
207	C₂³×C₄₇	—	2	2	no	—
208	C₂³×C₄₇	—	4	1	no	—
209	C₂³×C₄₇	—	4	2	no	—
210	C₂³×C₄₇	—	4	2	no	—
211	C₂³×C₄₇	—	4	2	no	—
212	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
215	Q₈×C₄₇	—	2	2	no	—
216	Q₈×C₄₇	—	2	2	no	—
217	Q₈×C₄₇	—	2	2	no	—
218	Q₈×C₄₇	—	4	2	no	—
219	D₄×C₄₇	—	2	2	no	—
220	D₄×C₄₇	—	2	2	no	—
221	D₄×C₄₇	—	2	2	no	—
222	D₄×C₄₇	—	4	2	no	—
223	D₄×C₄₇	—	4	2	no	—
224	D₄×C₄₇	—	4	4	no	—
225	D₄×C₄₇	—	4	2	no	—
226	D₄×C₄₇	—	4	2	no	—
227	D₄×C₄₇	—	4	2	no	—
228	D₄×C₄₇	—	4	2	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	2	1	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	4	4	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	1	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	4	1	no	—
246	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
251	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
252	C₂×Dic₄₇	—	2	4	no	—
253	C₂×Dic₄₇	—	4	2	no	—
254	C₂×Dic₄₇	—	4	2	no	—
255	C₈×C₄₇	—	2	2	no	—
256	C₈×C₄₇	—	2	2	no	—
257	C₄₇⋊C₈	—	2	1	no	—
258	C₄₇⋊C₈	—	2	1	no	—
259	C₄₇⋊C₈	—	2	1	no	—
260	C₄₇⋊C₈	—	2	1	no	—
261	C₄₇⋊C₈	—	4	1	no	—
262	C₄₇⋊C₈	—	4	2	no	—
263	C₄₇⋊C₈	—	4	1	no	—
264	#22060	—	47	1	no	maximal, Sylow
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	2	1	no	—
267	C₂²×C₄₇	—	2	1	no	—
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	1	no	—
270	C₂²×C₄₇	—	2	1	no	—
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	4	4	no	—
273	C₂²×C₄₇	—	4	2	no	—
274	C₂²×C₄₇	—	4	1	no	—
275	C₂²×C₄₇	—	4	1	no	—
276	C₂²×C₄₇	—	4	2	no	—
277	C₂²×C₄₇	—	4	1	no	—
278	C₂²×C₄₇	—	4	2	no	—
279	C₂²×C₄₇	—	8	4	no	—
280	C₂²×C₄₇	#443	1	2	yes	—
281	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂²×C₄₇	#538	1	2	yes	—
283	C₄×C₄₇	—	2	1	no	—
284	C₄×C₄₇	—	2	1	no	—
285	C₄×C₄₇	—	4	2	no	—
286	C₄×C₄₇	—	4	1	no	—
287	C₄×C₄₇	—	4	1	no	—
288	C₄×C₄₇	—	4	1	no	—
289	C₄×C₄₇	#518	1	2	yes	—
290	C₄×C₄₇	#534	1	1	yes	characteristic
291	C₄×C₄₇	#535	1	1	yes	characteristic
292	Dic₄₇	—	4	4	no	—
293	#3002	D₄₇	1	1	yes	characteristic
294	#2929	—	47	1	no	—
295	C₂×#408	—	47	1	no	—
296	#1974	—	47	2	no	—
297	#1937	—	47	2	no	—
298	#1929	—	47	2	no	—
299	#1876	—	47	2	no	—
300	#1871	—	47	1	no	—
301	#1855	—	47	1	no	—
302	#1789	—	47	1	no	—
303	C₈×C₂²⋊C₄	—	47	1	no	—
304	C₂×C₄₇	—	2	2	no	—
305	C₂×C₄₇	—	2	2	no	—
306	C₂×C₄₇	—	4	1	no	—
307	C₂×C₄₇	—	8	1	no	—
308	C₂×C₄₇	—	8	2	no	—
309	C₂×C₄₇	#2321	1	1	yes	characteristic
310	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
311	C₂×C₄₇	#2955	1	1	yes	characteristic
312	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
313	C₂×#135	C₂×D₄₇	1	2	yes	—
314	C₂×#131	—	47	1	no	—
315	C₂²×M₁₆	—	47	1	no	—
316	C₂³×C₈	—	47	1	no	—
317	#525	C₂×D₄₇	1	1	yes	characteristic
318	#452	Dic₄₇	1	2	yes	complemented
319	#451	Dic₄₇	1	1	yes	characteristic, complemented
320	#450	Dic₄₇	1	1	yes	characteristic, complemented
321	#449	Dic₄₇	1	2	yes	complemented
322	#448	Dic₄₇	1	1	yes	characteristic, complemented
323	#447	Dic₄₇	1	1	yes	characteristic, complemented
324	#435	—	94	1	no	—
325	#435	—	94	1	no	—
326	C₈×D₄	—	94	1	no	—
327	C₈×D₄	—	94	1	no	—
328	C₂×#108	—	47	2	no	—
329	#424	—	47	1	no	—
330	C₂×#104	—	47	2	no	—
331	C₂×#104	—	47	2	no	—
332	C₂×#104	—	47	2	no	—
333	#416	C₂×D₄₇	1	2	yes	—
334	#408	—	47	2	no	—
335	#408	—	47	2	no	—
336	#408	—	47	1	no	—
337	#408	—	94	1	no	—
338	#408	—	94	1	no	—
339	#407	—	47	1	no	—
340	C₂×C₂²⋊C₈	—	94	1	no	—
341	C₂×C₂²⋊C₈	—	94	1	no	—
342	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
343	#405	—	47	1	no	—
344	C₂×C₄×C₈	—	47	2	no	—
345	C₄×C₂²⋊C₄	—	47	1	no	—
346	#341	—	47	2	no	—
347	#339	—	47	2	no	—
348	#336	—	47	2	no	—
349	C₄₇	#22060	1	1	yes	characteristic, complemented, Sylow
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	4	2	no	—
353	C₂×#41	—	4	2	no	—
354	C₂×#41	C₂×Dic₄₇	1	2	yes	—
355	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
356	C₂×#41	C₂²×D₄₇	1	2	yes	—
357	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
362	#135	—	4	2	no	—
363	#135	—	4	2	no	—
364	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
365	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
366	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
367	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
368	#131	—	188	2	no	—
369	C₂×M₁₆	—	47	2	no	—
370	C₂×M₁₆	—	47	1	no	—
371	C₂×M₁₆	—	47	1	no	—
372	C₂×M₁₆	—	94	1	no	—
373	C₂×M₁₆	—	94	1	no	—
374	C₂×M₁₆	—	188	2	no	—
375	C₂²×C₈	—	47	1	no	—
376	C₂²×C₈	—	47	1	no	—
377	C₂²×C₈	—	47	1	no	—
378	C₂²×C₈	—	47	1	no	—
379	C₂²×C₈	—	47	1	no	—
380	C₂²×C₈	—	47	1	no	—
381	C₂²×C₈	—	94	1	no	—
382	C₂²×C₈	—	94	1	no	—
383	C₂²×C₈	—	188	2	no	—
384	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
385	#123	—	2	1	no	—
386	C₂²⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
387	C₂²⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
388	#121	C₂×Dic₄₇	1	1	yes	characteristic
389	#121	C₂×Dic₄₇	1	1	yes	characteristic
390	#120	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	#117	C₂²×D₄₇	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	94	1	no	—
395	C₂×C₄²	—	47	2	no	—
396	#108	—	188	2	no	—
397	C₄⋊C₈	—	94	1	no	—
398	C₄⋊C₈	—	94	1	no	—
399	#104	—	188	2	no	—
400	#104	—	188	2	no	—
401	#104	—	188	2	no	—
402	#103	C₂×Dic₄₇	1	2	yes	—
403	#103	C₂×Dic₄₇	1	2	yes	—
404	#102	C₂×Dic₄₇	1	2	yes	—
405	#102	C₂×Dic₄₇	1	2	yes	—
406	C₂²⋊C₈	—	94	2	no	—
407	C₂²⋊C₈	—	94	2	no	—
408	C₂²⋊C₈	—	94	2	no	—
409	C₂²⋊C₈	—	94	2	no	—
410	C₂²⋊C₈	—	94	1	no	—
411	C₂²⋊C₈	—	94	1	no	—
412	C₂²⋊C₈	—	94	1	no	—
413	C₂²⋊C₈	—	94	1	no	—
414	C₂²⋊C₈	C₂×Dic₄₇	1	1	yes	characteristic
415	C₂²⋊C₈	C₂×Dic₄₇	1	1	yes	characteristic
416	C₂²⋊C₈	C₂×Dic₄₇	1	2	yes	—
417	#97	—	94	1	no	—
418	C₄×C₈	—	94	1	no	—
419	C₄×C₈	—	188	2	no	—
420	#95	—	94	1	no	—
421	C₂⁴	—	2	1	no	—
422	C₂⁴	#10625352	1	1	yes	characteristic
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	4	2	no	—
430	#41	—	4	2	no	—
431	#41	—	4	4	no	—
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
437	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
447	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	94	2	no	—
457	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
459	C₂²×C₄	#10625352	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
461	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
462	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
463	Q₁₆	—	4	2	no	—
464	SD₁₆	—	4	2	no	—
465	SD₁₆	—	4	2	no	—
466	D₈	—	4	2	no	—
467	M₁₆	—	94	2	no	—
468	M₁₆	—	94	2	no	—
469	M₁₆	—	94	2	no	—
470	M₁₆	—	94	2	no	—
471	M₁₆	—	188	2	no	—
472	M₁₆	—	188	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	47	1	no	—
476	C₂×C₈	—	47	1	no	—
477	C₂×C₈	—	47	1	no	—
478	C₂×C₈	—	47	1	no	—
479	C₂×C₈	—	94	2	no	—
480	C₂×C₈	—	94	2	no	—
481	C₂×C₈	—	94	1	no	—
482	C₂×C₈	—	94	2	no	—
483	C₂×C₈	—	94	1	no	—
484	C₂×C₈	—	188	1	no	—
485	C₂×C₈	—	188	1	no	—
486	C₂×C₈	—	188	1	no	—
487	C₂×C₈	—	188	1	no	—
488	C₂×C₈	—	188	2	no	—
489	C₂×C₈	—	188	2	no	—
490	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
491	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	94	4	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	94	2	no	—
504	C₄²	—	94	2	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
514	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
515	C₂³	C₂×#10625352	1	1	yes	characteristic
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	2	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	4	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	94	4	no	—
548	C₂×C₄	—	188	2	no	—
549	C₂×C₄	—	188	2	no	—
550	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
551	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
553	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
554	C₂×C₄	#13094069	1	2	yes	—
555	C₂×C₄	#13094069	1	2	yes	—
556	C₈	—	2	2	no	—
557	C₈	—	2	2	no	—
558	C₈	—	94	1	no	—
559	C₈	—	94	1	no	—
560	C₈	—	94	1	no	—
561	C₈	—	94	1	no	—
562	C₈	—	188	1	no	—
563	C₈	—	188	2	no	—
564	C₈	—	188	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	8	4	no	—
580	C₂²	#15689240	1	2	yes	—
581	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
582	C₂²	#15689708	1	2	yes	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	188	4	no	—
590	C₄	#15689598	1	2	yes	—
591	C₄	#15689683	1	1	yes	characteristic
592	C₄	#15689688	1	1	yes	characteristic
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	4	1	no	—
596	C₂	—	8	2	no	—
597	C₂	—	8	1	no	—
598	C₂	#20246049	1	1	yes	characteristic
599	C₂	C₂×#15689240	1	1	yes	characteristic
600	C₂	#20252291	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3002	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3002	D₄₇
hypocenter	C₄₇	#22060
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3002

Complements

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

N	H ≅ G/N	type
1. #20252083	C₂	semidirect
2. C₂×#15689090	C₂	semidirect
3. #20244277	C₂	semidirect
4. #20244094	C₂	semidirect
5. #20244038	C₂	semidirect
6. #20243717	C₂	semidirect
7. #20243691	C₂	semidirect
8. #20243595	C₂	semidirect
9. #20243332	C₂	semidirect
10. #20243162	C₂	semidirect
12. C₂×#13094031	C₂²	semidirect
19. C₂×#13093960	C₂²	semidirect
20. #15689150	C₂²	semidirect
23. C₂×#13093951	C₂²	semidirect
28. #15689090	C₂²	semidirect
32. #15689079	C₂²	semidirect
33. C₂×C₈×Dic₄₇	C₂²	semidirect
35. #15688888	C₂²	semidirect
36. #15688882	C₂²	semidirect
37. #15688877	C₂²	semidirect
41. C₄₇×#452	C₄	semidirect
42. C₄₇×#451	C₄	semidirect
43. C₄₇×#450	C₄	semidirect
44. C₄₇×#449	C₄	semidirect
45. C₄₇×#448	C₄	semidirect
46. C₄₇×#447	C₄	semidirect
318. #452	Dic₄₇	semidirect
319. #451	Dic₄₇	semidirect
320. #450	Dic₄₇	semidirect
321. #449	Dic₄₇	semidirect
322. #448	Dic₄₇	semidirect
323. #447	Dic₄₇	semidirect
349. C₄₇	#22060	semidirect

Maximal subgroups

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

subgroup	index
#20252083	2
C₂×#15689090	2
#20244277	2
#20244094	2
#20244038	2
#20243717	2
#20243691	2
#20243595	2
#20243332	2
#20243162	2
C₄₇×#3002	2
#22060	47