Subgroups — #26223122

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689245	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252083	C₂	1	2	yes	maximal, complemented
3	C₂×#15689081	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244277	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244137	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244094	C₂	1	2	yes	maximal, complemented
7	#20243837	C₂	1	2	yes	maximal, complemented
8	#20243430	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243274	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243235	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3054	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	—
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×#13093983	C₂²	1	1	yes	characteristic
15	#15689245	—	2	4	no	—
16	#15689195	—	2	4	no	—
17	D₄×C₄₇⋊C₈	—	2	4	no	—
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	C₂×#13093960	C₂²	1	1	yes	characteristic
20	#15689150	C₂²	1	2	yes	—
21	C₂×#13093951	C₂²	1	2	yes	—
22	C₂×#13093951	C₂²	1	2	yes	—
23	#15689090	C₂²	1	2	yes	—
24	#15689087	C₂²	1	2	yes	—
25	#15689081	—	2	4	no	—
26	#15689079	C₂²	1	2	yes	—
27	C₂×#13093934	C₂²	1	1	yes	characteristic
28	C₂×#13093934	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688888	C₂²	1	2	yes	—
32	#15688882	C₂²	1	2	yes	—
33	#15688882	C₂²	1	2	yes	—
34	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#525	C₂²	1	2	yes	—
37	C₄₇×#470	C₄	1	2	yes	complemented
38	C₄₇×#469	C₄	1	2	yes	complemented
39	C₄₇×#468	C₄	1	4	yes	complemented
40	C₄₇×#427	C₂²	1	1	yes	characteristic
41	C₄₇×#416	C₂²	1	2	yes	—
42	#13094031	—	2	4	no	—
43	#13094031	—	2	4	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	C₂³	1	2	yes	—
46	C₂×#10625329	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	—	2	2	no	—
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	—	2	2	no	—
50	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	#13093983	—	2	2	no	—
54	#13093983	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	#13093960	—	2	2	no	—
60	#13093960	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
62	#13093951	—	2	4	no	—
63	#13093951	—	2	4	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
66	#13093935	—	2	2	no	—
67	#13093934	—	2	2	no	—
68	#13093934	D₄	1	4	yes	complemented
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	—	2	2	no	—
72	C₂×#41×C₄₇	C₂³	1	2	yes	—
73	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
74	#135×C₄₇	—	2	2	no	—
75	#135×C₄₇	—	2	2	no	—
76	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×M₁₆×C₄₇	—	2	2	no	—
80	C₂×M₁₆×C₄₇	—	2	2	no	—
81	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	#123×C₄₇	—	2	2	no	—
86	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
87	#121×C₄₇	C₂×C₄	1	4	yes	—
88	#120×C₄₇	—	2	2	no	—
89	C₄×D₄×C₄₇	—	2	4	no	—
90	#117×C₄₇	C₂³	1	2	yes	—
91	#107×C₄₇	C₂×C₄	1	2	yes	—
92	#106×C₄₇	C₂×C₄	1	2	yes	—
93	#103×C₄₇	C₂×C₄	1	4	yes	—
94	#102×C₄₇	C₂×C₄	1	4	yes	—
95	C₂⁴×C₄₇	#41	1	1	yes	characteristic
96	#41×C₄₇	—	2	2	no	—
97	#41×C₄₇	—	2	2	no	—
98	#41×C₄₇	—	2	2	no	—
99	#41×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₇	—	2	1	no	—
114	C₂²×Dic₄₇	—	2	1	no	—
115	Q₁₆×C₄₇	—	2	2	no	—
116	SD₁₆×C₄₇	—	2	4	no	—
117	D₈×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	2	4	no	—
119	M₁₆×C₄₇	—	2	4	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₇	#41	1	2	yes	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
129	C₂²⋊C₄×C₄₇	—	2	4	no	—
130	C₂²⋊C₄×C₄₇	—	2	2	no	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₂²⋊Dic₄₇	—	2	4	no	—
134	C₄⋊Dic₄₇	—	2	4	no	—
135	C₄×Dic₄₇	—	2	1	no	—
136	C₄×Dic₄₇	—	2	1	no	—
137	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
138	C₄×Dic₄₇	#41	1	2	yes	—
139	#10625329	—	2	2	no	—
140	#10625329	—	2	2	no	—
141	#10625329	—	2	2	no	—
142	#10625329	—	2	2	no	—
143	#10625329	—	4	4	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	8	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	4	4	no	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₄₇⋊C₈	#41	1	2	yes	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	4	2	no	—
158	C₂³×C₄₇	C₄×D₄	1	2	yes	—
159	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
160	Q₈×C₄₇	—	2	2	no	—
161	Q₈×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	2	2	no	—
164	D₄×C₄₇	—	4	8	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	C₄×D₄	1	2	yes	—
190	C₈×C₄₇	C₄×D₄	1	2	yes	—
191	C₄₇⋊C₈	—	2	2	no	—
192	C₄₇⋊C₈	—	4	2	no	—
193	C₄₇⋊C₈	—	4	2	no	—
194	C₄₇⋊C₈	#121	1	4	yes	—
195	#21550	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	2	4	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	—	4	4	no	—
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₄₇	#525	1	1	yes	characteristic
205	C₂²×C₄₇	#529	1	1	yes	characteristic
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	4	4	no	—
208	C₄×C₄₇	—	4	2	no	—
209	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
211	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
212	C₄×C₄₇	#532	1	1	yes	characteristic
213	Dic₄₇	—	4	2	no	—
214	Dic₄₇	—	4	2	no	—
215	#3054	D₄₇	1	1	yes	characteristic
216	C₂×#444	—	47	1	no	—
217	#2929	—	47	2	no	—
218	C₂×#405	—	47	1	no	—
219	#1974	—	47	1	no	—
220	#1945	—	47	1	no	—
221	#1937	—	47	2	no	—
222	#1897	—	47	2	no	—
223	#1811	—	47	1	no	—
224	#1773	—	47	1	no	—
225	#1765	—	47	2	no	—
226	C₂×C₄₇	—	2	1	no	—
227	C₂×C₄₇	—	2	1	no	—
228	C₂×C₄₇	—	4	2	no	—
229	C₂×C₄₇	—	8	2	no	—
230	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
231	C₂×C₄₇	#2955	1	2	yes	—
232	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
233	C₂×#131	—	47	2	no	—
234	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
235	C₂³×C₈	—	47	1	no	—
236	#525	C₂×D₄₇	1	2	yes	—
237	C₂×#117	—	47	1	no	—
238	#470	Dic₄₇	1	2	yes	complemented
239	#469	Dic₄₇	1	2	yes	complemented
240	#468	Dic₄₇	1	4	yes	complemented
241	#444	—	94	4	no	—
242	#435	—	94	4	no	—
243	C₈×D₄	—	94	4	no	—
244	C₂×#108	—	47	1	no	—
245	C₂×#108	—	47	1	no	—
246	#427	C₂×D₄₇	1	1	yes	characteristic
247	#424	—	47	2	no	—
248	C₂×#104	—	47	2	no	—
249	C₂×#104	—	47	2	no	—
250	#416	C₂×D₄₇	1	2	yes	—
251	#408	—	47	2	no	—
252	#407	—	47	2	no	—
253	#405	—	47	2	no	—
254	#405	—	94	4	no	—
255	C₂×#97	—	47	1	no	—
256	C₂×#97	—	47	1	no	—
257	C₂×C₄×C₈	—	47	1	no	—
258	C₂×C₄×C₈	—	47	1	no	—
259	#341	—	47	2	no	—
260	#339	—	47	2	no	—
261	#339	—	47	2	no	—
262	C₄₇	#21550	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	C₂²×D₄₇	1	2	yes	—
264	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
265	#135	—	2	2	no	—
266	#135	—	2	2	no	—
267	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
268	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
269	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
270	#131	—	94	4	no	—
271	#131	—	94	4	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	47	2	no	—
275	C₂×M₁₆	—	47	2	no	—
276	C₂×M₁₆	—	94	2	no	—
277	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
278	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
279	C₂²×C₈	—	47	1	no	—
280	C₂²×C₈	—	47	4	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	94	2	no	—
283	C₂²×C₈	—	94	2	no	—
284	C₂²×C₈	—	94	2	no	—
285	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
287	#123	—	2	2	no	—
288	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
289	#121	C₂×Dic₄₇	1	4	yes	—
290	#120	—	2	2	no	—
291	C₄×D₄	—	2	4	no	—
292	#117	—	94	2	no	—
293	#117	—	94	2	no	—
294	#117	C₂²×D₄₇	1	2	yes	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₂²⋊C₄	—	94	1	no	—
297	C₂×C₄²	—	47	1	no	—
298	C₂×C₄²	—	47	1	no	—
299	#108	—	94	2	no	—
300	#108	—	94	2	no	—
301	#107	C₂×Dic₄₇	1	2	yes	—
302	#106	C₂×Dic₄₇	1	2	yes	—
303	C₄⋊C₈	—	94	4	no	—
304	#104	—	94	4	no	—
305	#104	—	94	4	no	—
306	#103	C₂×Dic₄₇	1	4	yes	—
307	#102	C₂×Dic₄₇	1	4	yes	—
308	C₂²⋊C₈	—	94	4	no	—
309	C₂²⋊C₈	—	94	4	no	—
310	#97	—	47	4	no	—
311	#97	—	94	2	no	—
312	#97	—	94	2	no	—
313	C₄×C₈	—	94	2	no	—
314	C₄×C₈	—	94	2	no	—
315	C₄×C₈	—	94	2	no	—
316	C₂⁴	#10625352	1	1	yes	characteristic
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	94	1	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	D₄×D₄₇	1	2	yes	—
333	C₂²×C₄	#10625352	1	1	yes	characteristic
334	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
335	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
336	Q₁₆	—	2	2	no	—
337	SD₁₆	—	2	4	no	—
338	D₈	—	2	2	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	—	94	2	no	—
342	M₁₆	—	94	2	no	—
343	M₁₆	—	94	2	no	—
344	M₁₆	—	94	2	no	—
345	M₁₆	—	188	4	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	47	2	no	—
349	C₂×C₈	—	47	2	no	—
350	C₂×C₈	—	47	2	no	—
351	C₂×C₈	—	47	2	no	—
352	C₂×C₈	—	94	8	no	—
353	C₂×C₈	—	94	1	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	188	4	no	—
358	C₂×C₈	D₄×D₄₇	1	2	yes	—
359	C₂×C₈	#10625352	1	2	yes	—
360	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
361	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
362	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	94	4	no	—
365	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	94	4	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	47	2	no	—
372	C₄²	—	47	2	no	—
373	C₄²	—	94	1	no	—
374	C₄²	—	94	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	D₄×Dic₄₇	1	2	yes	—
380	C₂³	C₂×#10625352	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	94	2	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	188	2	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
403	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
406	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
407	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	47	4	no	—
411	C₈	—	94	2	no	—
412	C₈	—	188	2	no	—
413	C₈	—	188	2	no	—
414	C₈	D₄×Dic₄₇	1	2	yes	—
415	C₈	D₄×Dic₄₇	1	2	yes	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	2	no	—
423	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
424	C₂²	#15689633	1	1	yes	characteristic
425	C₂²	#15689654	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	188	2	no	—
430	C₄	—	188	2	no	—
431	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
432	C₄	#41×Dic₄₇	1	1	yes	characteristic
433	C₄	#121×D₄₇	1	1	yes	characteristic
434	C₄	#15689668	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	4	2	no	—
438	C₂	—	8	2	no	—
439	C₂	#121×Dic₄₇	1	1	yes	characteristic
440	C₂	#20252291	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3054	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3054	D₄₇
hypocenter	C₄₇	#21550
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3054

Complements

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

N	H ≅ G/N	type
1. C₂×#15689245	C₂	semidirect
2. #20252083	C₂	semidirect
3. C₂×#15689081	C₂	semidirect
4. #20244277	C₂	semidirect
5. #20244137	C₂	semidirect
6. #20244094	C₂	semidirect
7. #20243837	C₂	semidirect
8. #20243430	C₂	semidirect
9. #20243274	C₂	semidirect
10. #20243235	C₂	semidirect
37. C₄₇×#470	C₄	semidirect
38. C₄₇×#469	C₄	semidirect
39. C₄₇×#468	C₄	semidirect
68. #13093934	D₄	semidirect
238. #470	Dic₄₇	semidirect
239. #469	Dic₄₇	semidirect
240. #468	Dic₄₇	semidirect
262. C₄₇	#21550	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689245	2
#20252083	2
C₂×#15689081	2
#20244277	2
#20244137	2
#20244094	2
#20243837	2
#20243430	2
#20243274	2
#20243235	2
C₄₇×#3054	2
#21550	47