Subgroups — #26227673

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	#20252604	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689089	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244275	C₂	1	2	yes	maximal, complemented
4	#20244091	C₂	1	2	yes	maximal, complemented
5	#20244036	C₂	1	2	yes	maximal, complemented
6	#20243715	C₂	1	2	yes	maximal, complemented
7	#20243691	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243592	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625350	C₂²	1	1	yes	characteristic
13	C₂×#13094044	C₂²	1	2	yes	—
14	C₂²×#10625329	C₂²	1	1	yes	characteristic
15	#15689283	C₄	1	2	yes	complemented
16	#15689278	C₄	1	1	yes	characteristic, complemented
17	#15689273	C₄	1	1	yes	characteristic, complemented
18	#15689266	C₄	1	2	yes	complemented
19	#15689261	C₄	1	1	yes	characteristic, complemented
20	#15689256	C₄	1	1	yes	characteristic, complemented
21	C₂×#13093959	C₂²	1	2	yes	complemented
22	C₂×#13093951	C₂²	1	2	yes	complemented
23	C₂×#13093950	C₂²	1	2	yes	—
24	C₂×#13093950	C₂²	1	2	yes	—
25	#15689117	C₂²	1	2	yes	—
26	#15689089	—	2	1	no	—
27	#15689089	—	2	1	no	—
28	#15689089	C₂²	1	2	yes	—
29	#15689089	C₂²	1	2	yes	—
30	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
32	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
33	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
34	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688887	C₂²	1	2	yes	complemented
36	#15688882	C₂²	1	2	yes	complemented
37	#15688877	C₂²	1	2	yes	complemented
38	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic, complemented
39	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#525	C₂²	1	1	yes	characteristic
41	C₄₇×#435	—	2	1	no	—
42	C₄₇×#435	—	2	1	no	—
43	C₈×D₄×C₄₇	—	2	1	no	—
44	C₈×D₄×C₄₇	—	2	1	no	—
45	C₄₇×#424	C₂²	1	1	yes	characteristic, complemented
46	C₄₇×#408	C₂²	1	1	yes	characteristic, complemented
47	C₄₇×#407	C₂²	1	1	yes	characteristic
48	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
49	C₂×#10625350	—	2	1	no	—
50	C₂×#10625350	—	2	1	no	—
51	C₂×#10625350	—	4	2	no	—
52	C₂×#10625350	—	4	2	no	—
53	C₂×#10625350	C₂×C₄	1	2	yes	—
54	C₂×#10625350	C₂³	1	2	yes	—
55	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₂²⋊D₄₇	—	2	1	no	—
58	C₂²×C₄×D₄₇	—	2	1	no	—
59	#13094044	—	4	2	no	—
60	#13094044	—	4	2	no	—
61	C₂×#10625337	C₂×C₄	1	2	yes	—
62	C₂×#10625335	C₂×C₄	1	2	yes	—
63	C₂×#10625336	C₂×C₄	1	2	yes	—
64	C₂×#10625334	C₂×C₄	1	2	yes	—
65	C₂×#10625329	—	2	1	no	—
66	C₂×#10625329	—	4	2	no	—
67	C₂×#10625329	C₂³	1	2	yes	—
68	C₂²×C₄₇⋊C₈	—	2	1	no	—
69	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
70	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
71	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
72	#13093959	—	4	2	no	—
73	#13093951	—	4	2	no	—
74	#13093950	—	4	2	no	—
75	#13093950	—	4	2	no	—
76	#13093947	C₂×C₄	1	2	yes	—
77	#13093947	C₂×C₄	1	2	yes	—
78	#13093944	C₂×C₄	1	2	yes	—
79	#13093944	C₂×C₄	1	2	yes	—
80	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
83	(C₂×D₄₇)⋊C₈	—	2	2	no	—
84	(C₂×D₄₇)⋊C₈	—	2	2	no	—
85	(C₂×D₄₇)⋊C₈	—	2	2	no	—
86	(C₂×D₄₇)⋊C₈	—	2	2	no	—
87	C₈×Dic₄₇	—	4	2	no	—
88	C₄₇⋊#95	—	2	1	no	—
89	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	#131×C₄₇	—	4	2	no	—
92	C₂×M₁₆×C₄₇	—	2	1	no	—
93	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₄₇	—	2	1	no	—
96	C₂²×C₈×C₄₇	—	4	2	no	—
97	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
101	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	#123×C₄₇	—	2	1	no	—
104	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
106	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
107	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
108	#120×C₄₇	—	2	1	no	—
109	C₄×D₄×C₄₇	—	2	1	no	—
110	C₄×D₄×C₄₇	—	2	1	no	—
111	#117×C₄₇	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₄₇	—	2	1	no	—
113	C₄⋊C₈×C₄₇	—	2	1	no	—
114	C₂²⋊C₈×C₄₇	—	2	1	no	—
115	C₂²⋊C₈×C₄₇	—	2	1	no	—
116	C₂²⋊C₈×C₄₇	—	2	1	no	—
117	C₂²⋊C₈×C₄₇	—	2	1	no	—
118	#97×C₄₇	—	2	1	no	—
119	C₄×C₈×C₄₇	—	2	1	no	—
120	C₂⁴×C₄₇	#41	1	1	yes	characteristic
121	C₂³×D₄₇	—	2	1	no	—
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	2	no	—
124	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₄₇	—	2	1	no	—
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂×C₂²⋊D₄₇	—	2	2	no	—
139	C₂×C₂²⋊D₄₇	—	2	2	no	—
140	C₂×C₂²⋊D₄₇	—	4	4	no	—
141	C₂²×Dic₄₇	—	2	1	no	—
142	C₂²×Dic₄₇	—	2	2	no	—
143	#10625350	—	2	2	no	—
144	#10625350	—	2	2	no	—
145	#10625350	—	2	2	no	—
146	#10625350	—	2	2	no	—
147	#10625350	—	4	2	no	—
148	#10625350	—	4	2	no	—
149	#10625350	—	4	4	no	—
150	#10625350	—	4	2	no	—
151	#10625350	—	4	2	no	—
152	C₂×D₁₈₈	—	2	1	no	—
153	C₂×D₁₈₈	—	4	2	no	—
154	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
155	C₂×C₄×D₄₇	—	2	2	no	—
156	C₂×C₄×D₄₇	—	2	2	no	—
157	C₂×C₄×D₄₇	—	4	2	no	—
158	C₂×C₄×D₄₇	—	4	2	no	—
159	C₂×Dic₉₄	—	2	1	no	—
160	C₂×Dic₉₄	—	4	2	no	—
161	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
162	M₁₆×C₄₇	—	2	2	no	—
163	M₁₆×C₄₇	—	2	2	no	—
164	M₁₆×C₄₇	—	4	2	no	—
165	C₂×C₈×C₄₇	—	2	2	no	—
166	C₂×C₈×C₄₇	—	2	2	no	—
167	C₂×C₈×C₄₇	—	2	1	no	—
168	C₂×C₈×C₄₇	—	2	1	no	—
169	C₂×C₈×C₄₇	—	4	1	no	—
170	C₂×C₈×C₄₇	—	4	1	no	—
171	C₂×C₈×C₄₇	—	4	1	no	—
172	C₂×C₈×C₄₇	—	4	1	no	—
173	C₂×C₈×C₄₇	—	4	2	no	—
174	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₄⋊C₄×C₄₇	—	2	1	no	—
179	C₄⋊C₄×C₄₇	—	2	1	no	—
180	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²⋊C₄×C₄₇	—	2	1	no	—
183	C₂²⋊C₄×C₄₇	—	2	1	no	—
184	C₂²⋊C₄×C₄₇	—	2	1	no	—
185	C₂²⋊C₄×C₄₇	—	2	1	no	—
186	C₂²⋊C₄×C₄₇	—	2	1	no	—
187	C₄²×C₄₇	—	2	1	no	—
188	C₂²⋊Dic₄₇	—	2	4	no	—
189	#10625337	—	4	2	no	—
190	#10625336	—	4	2	no	—
191	#10625335	—	4	2	no	—
192	#10625334	—	4	2	no	—
193	C₄×Dic₄₇	—	2	2	no	—
194	C₄×Dic₄₇	—	2	2	no	—
195	#10625329	—	2	2	no	—
196	#10625329	—	2	2	no	—
197	#10625329	—	4	2	no	—
198	C₂×C₄₇⋊C₈	—	2	2	no	—
199	C₂×C₄₇⋊C₈	—	2	2	no	—
200	C₂×C₄₇⋊C₈	—	2	2	no	—
201	C₂×C₄₇⋊C₈	—	4	2	no	—
202	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
203	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	2	1	no	—
207	C₂³×C₄₇	—	4	1	no	—
208	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
211	C₂²×D₄₇	—	2	2	no	—
212	C₂²×D₄₇	—	4	2	no	—
213	C₂²×D₄₇	—	4	2	no	—
214	C₂²×D₄₇	—	4	2	no	—
215	Q₈×C₄₇	—	2	2	no	—
216	D₄×C₄₇	—	2	2	no	—
217	D₄×C₄₇	—	4	2	no	—
218	D₄×C₄₇	—	4	2	no	—
219	D₄×C₄₇	—	4	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	1	no	—
224	C₂×C₄×C₄₇	—	2	1	no	—
225	C₂×C₄×C₄₇	—	2	1	no	—
226	C₂×C₄×C₄₇	—	2	1	no	—
227	C₂×C₄×C₄₇	—	2	1	no	—
228	C₂×C₄×C₄₇	—	2	1	no	—
229	C₂×C₄×C₄₇	—	2	1	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
237	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
238	C₂²⋊D₄₇	—	4	4	no	—
239	C₂²⋊D₄₇	—	4	2	no	—
240	C₂²⋊D₄₇	—	4	2	no	—
241	C₂×Dic₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	2	2	no	—
243	C₂×Dic₄₇	—	4	2	no	—
244	C₂×Dic₄₇	—	4	2	no	—
245	C₂×Dic₄₇	—	4	2	no	—
246	D₁₈₈	—	2	2	no	—
247	D₁₈₈	—	2	2	no	—
248	D₁₈₈	—	4	2	no	—
249	C₄×D₄₇	—	4	4	no	—
250	C₄×D₄₇	—	4	2	no	—
251	C₄×D₄₇	—	4	2	no	—
252	Dic₉₄	—	2	2	no	—
253	Dic₉₄	—	2	2	no	—
254	Dic₉₄	—	4	2	no	—
255	C₈×C₄₇	—	2	1	no	—
256	C₈×C₄₇	—	2	1	no	—
257	C₈×C₄₇	—	2	1	no	—
258	C₈×C₄₇	—	2	1	no	—
259	C₈×C₄₇	—	4	1	no	—
260	C₈×C₄₇	—	4	1	no	—
261	C₄₇⋊C₈	—	2	2	no	—
262	C₄₇⋊C₈	—	2	2	no	—
263	C₄₇⋊C₈	—	4	2	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	1	no	—
274	C₂²×C₄₇	—	4	1	no	—
275	C₂²×C₄₇	—	4	1	no	—
276	C₂²×C₄₇	#443	1	2	yes	—
277	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
278	C₂²×C₄₇	#538	1	2	yes	—
279	C₂×D₄₇	—	4	2	no	—
280	C₂×D₄₇	—	4	2	no	—
281	C₂×D₄₇	—	4	2	no	—
282	C₂×D₄₇	—	8	4	no	—
283	C₄×C₄₇	—	2	1	no	—
284	C₄×C₄₇	—	2	1	no	—
285	C₄×C₄₇	—	4	1	no	—
286	C₄×C₄₇	—	4	1	no	—
287	C₄×C₄₇	—	4	1	no	—
288	C₄×C₄₇	#518	1	2	yes	—
289	C₄×C₄₇	#534	1	1	yes	characteristic
290	C₄×C₄₇	#535	1	1	yes	characteristic
291	Dic₄₇	—	4	4	no	—
292	Dic₄₇	—	4	2	no	—
293	#3002	—	47	1	no	—
294	#2929	D₄₇	1	1	yes	characteristic, complemented
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	#2321	1	1	yes	characteristic
309	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
310	C₂×C₄₇	#2955	1	1	yes	characteristic
311	D₄₇	—	8	2	no	—
312	C₂²×#41	—	47	1	no	—
313	C₂×#135	—	47	2	no	—
314	C₂×#131	C₂×D₄₇	1	1	yes	characteristic, complemented
315	C₂²×M₁₆	—	47	1	no	—
316	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
317	#525	C₂×D₄₇	1	1	yes	characteristic
318	#452	—	47	2	no	—
319	#451	—	47	1	no	—
320	#450	—	47	1	no	—
321	#449	—	47	2	no	—
322	#448	—	47	1	no	—
323	#447	—	47	1	no	—
324	#435	—	2	1	no	—
325	#435	—	2	1	no	—
326	C₈×D₄	—	2	1	no	—
327	C₈×D₄	—	2	1	no	—
328	C₂×#108	—	47	2	no	—
329	#424	C₂×D₄₇	1	1	yes	characteristic, complemented
330	C₂×#104	—	47	2	no	—
331	C₂×#104	—	47	2	no	—
332	C₂×#104	—	47	2	no	—
333	#416	—	47	2	no	—
334	#408	—	47	2	no	—
335	#408	—	47	2	no	—
336	#408	—	94	1	no	—
337	#408	—	94	1	no	—
338	#408	C₂×D₄₇	1	1	yes	characteristic, complemented
339	#407	C₂×D₄₇	1	1	yes	characteristic
340	C₂×C₂²⋊C₈	—	47	1	no	—
341	C₂×C₂²⋊C₈	—	94	1	no	—
342	C₂×C₂²⋊C₈	—	94	1	no	—
343	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
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	—	47	2	no	—
351	C₂×#41	—	47	2	no	—
352	C₂×#41	—	94	1	no	—
353	C₂×#41	—	94	1	no	—
354	C₂×#41	—	188	2	no	—
355	C₂×#41	—	188	2	no	—
356	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
357	C₂²×Q₈	—	47	1	no	—
358	C₂²×D₄	—	47	1	no	—
359	C₂²×D₄	—	94	1	no	—
360	C₂³×C₄	—	94	1	no	—
361	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
362	#135	—	188	2	no	—
363	#135	—	188	2	no	—
364	C₂×Q₁₆	—	47	2	no	—
365	C₂×SD₁₆	—	47	2	no	—
366	C₂×SD₁₆	—	47	2	no	—
367	C₂×D₈	—	47	2	no	—
368	#131	—	4	2	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	47	2	no	—
371	C₂×M₁₆	—	94	1	no	—
372	C₂×M₁₆	—	188	2	no	—
373	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
374	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	4	2	no	—
377	C₂²×C₈	—	47	2	no	—
378	C₂²×C₈	—	94	1	no	—
379	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
380	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
381	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
383	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
384	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
385	#123	—	2	1	no	—
386	C₂²⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
387	C₂²⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
388	#121	C₄×D₄₇	1	1	yes	characteristic
389	#121	C₄×D₄₇	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	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	#104	—	188	2	no	—
400	#104	—	188	2	no	—
401	#104	—	188	2	no	—
402	#103	—	47	2	no	—
403	#103	—	47	2	no	—
404	#102	—	47	2	no	—
405	#102	—	47	2	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	47	1	no	—
411	C₂²⋊C₈	—	47	1	no	—
412	C₂²⋊C₈	—	47	2	no	—
413	C₂²⋊C₈	—	94	2	no	—
414	C₂²⋊C₈	—	94	2	no	—
415	C₂²⋊C₈	—	94	2	no	—
416	C₂²⋊C₈	—	94	2	no	—
417	#97	—	2	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	188	2	no	—
420	#95	—	94	1	no	—
421	C₂⁴	—	94	1	no	—
422	C₂⁴	#10625350	1	1	yes	characteristic
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	94	2	no	—
426	#41	—	94	2	no	—
427	#41	—	94	2	no	—
428	#41	—	94	2	no	—
429	#41	—	188	2	no	—
430	#41	—	188	2	no	—
431	#41	—	188	4	no	—
432	#41	—	188	2	no	—
433	#41	—	188	2	no	—
434	C₂×Q₈	—	47	2	no	—
435	C₂×Q₈	—	94	1	no	—
436	C₂×Q₈	—	188	2	no	—
437	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	47	2	no	—
442	C₂×D₄	—	94	2	no	—
443	C₂×D₄	—	94	2	no	—
444	C₂×D₄	—	94	1	no	—
445	C₂×D₄	—	188	2	no	—
446	C₂×D₄	—	188	4	no	—
447	C₂×D₄	C₂×C₄×D₄₇	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	—	94	1	no	—
452	C₂²×C₄	—	94	2	no	—
453	C₂²×C₄	—	94	2	no	—
454	C₂²×C₄	—	94	2	no	—
455	C₂²×C₄	—	188	2	no	—
456	C₂²×C₄	—	188	2	no	—
457	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
459	C₂²×C₄	#10625350	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
462	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
463	Q₁₆	—	188	2	no	—
464	SD₁₆	—	188	2	no	—
465	SD₁₆	—	188	2	no	—
466	D₈	—	188	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	4	2	no	—
470	M₁₆	—	94	2	no	—
471	M₁₆	—	94	2	no	—
472	M₁₆	—	188	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	2	no	—
482	C₂×C₈	—	47	2	no	—
483	C₂×C₈	—	47	2	no	—
484	C₂×C₈	—	94	2	no	—
485	C₂×C₈	—	94	2	no	—
486	C₂×C₈	—	94	2	no	—
487	C₂×C₈	—	188	2	no	—
488	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
489	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
490	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
491	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂×C₄×D₄₇	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	—	4	1	no	—
509	C₂³	—	94	2	no	—
510	C₂³	—	188	2	no	—
511	C₂³	—	188	2	no	—
512	C₂³	—	188	2	no	—
513	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
514	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
515	C₂³	C₂×#10625350	1	1	yes	characteristic
516	Q₈	—	2	2	no	—
517	Q₈	—	94	2	no	—
518	Q₈	—	94	2	no	—
519	Q₈	—	188	2	no	—
520	D₄	—	2	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	94	2	no	—
525	D₄	—	94	2	no	—
526	D₄	—	188	2	no	—
527	D₄	—	188	4	no	—
528	D₄	—	188	2	no	—
529	D₄	—	188	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	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	94	4	no	—
543	C₂×C₄	—	94	2	no	—
544	C₂×C₄	—	188	4	no	—
545	C₂×C₄	—	188	2	no	—
546	C₂×C₄	—	188	2	no	—
547	C₂×C₄	—	188	2	no	—
548	C₂×C₄	—	188	2	no	—
549	C₂×C₄	—	188	2	no	—
550	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
551	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
554	C₂×C₄	#13094069	1	2	yes	—
555	C₂×C₄	#13094070	1	2	yes	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	94	2	no	—
563	C₈	—	94	2	no	—
564	C₈	—	188	2	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	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	376	4	no	—
577	C₂²	—	188	2	no	—
578	C₂²	—	188	2	no	—
579	C₂²	—	188	2	no	—
580	C₂²	#15689238	1	2	yes	—
581	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
582	C₂²	#15689706	1	2	yes	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	188	4	no	—
589	C₄	—	188	2	no	—
590	C₄	#15689595	1	2	yes	—
591	C₄	#15689682	1	1	yes	characteristic
592	C₄	#15689687	1	1	yes	characteristic
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	4	1	no	—
596	C₂	—	8	1	no	—
597	C₂	—	376	2	no	—
598	C₂	#20246042	1	1	yes	characteristic
599	C₂	C₂×#15689238	1	1	yes	characteristic
600	C₂	#20252289	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2929	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252604	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2929	D₄₇
hypocenter	C₄₇	#22060
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ #2929

Complements

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

N	H ≅ G/N	type
2. C₂×#15689089	C₂	semidirect
3. #20244275	C₂	semidirect
4. #20244091	C₂	semidirect
5. #20244036	C₂	semidirect
6. #20243715	C₂	semidirect
7. #20243691	C₂	semidirect
8. #20243592	C₂	semidirect
9. #20243331	C₂	semidirect
10. C₈×C₂²⋊Dic₄₇	C₂	semidirect
11. C₄₇×#2929	C₂	semidirect
15. #15689283	C₄	semidirect
16. #15689278	C₄	semidirect
17. #15689273	C₄	semidirect
18. #15689266	C₄	semidirect
19. #15689261	C₄	semidirect
20. #15689256	C₄	semidirect
21. C₂×#13093959	C₂²	semidirect
22. C₂×#13093951	C₂²	semidirect
33. C₂×C₈×Dic₄₇	C₂²	semidirect
35. #15688887	C₂²	semidirect
36. #15688882	C₂²	semidirect
37. #15688877	C₂²	semidirect
38. C₂×#131×C₄₇	C₂²	semidirect
45. C₄₇×#424	C₂²	semidirect
46. C₄₇×#408	C₂²	semidirect
48. C₄₇×#405	C₂²	semidirect
294. #2929	D₄₇	semidirect
314. C₂×#131	C₂×D₄₇	semidirect
329. #424	C₂×D₄₇	semidirect
338. #408	C₂×D₄₇	semidirect
343. #405	C₂×D₄₇	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
#20252604	2
C₂×#15689089	2
#20244275	2
#20244091	2
#20244036	2
#20243715	2
#20243691	2
#20243592	2
#20243331	2
C₈×C₂²⋊Dic₄₇	2
C₄₇×#2929	2
#22060	47