Subgroups — #26223057

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252970	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689241	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252084	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244274	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244137	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244093	C₂	1	2	yes	maximal, complemented
8	#20243830	C₂	1	2	yes	maximal, complemented
9	#20243423	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243227	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094030	C₂²	1	2	yes	—
14	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
16	#15689635	C₂²	1	2	yes	—
17	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
18	#15689365	C₄	1	2	yes	complemented
19	#15689360	C₄	1	2	yes	complemented
20	#15689353	C₄	1	4	yes	complemented
21	#15689241	—	2	4	no	—
22	#15689196	—	2	4	no	—
23	C₈×D₁₈₈	—	2	4	no	—
24	C₂×#13093960	C₂²	1	1	yes	characteristic
25	#15689150	C₂²	1	2	yes	—
26	C₂×#13093952	C₂²	1	2	yes	—
27	C₂×#13093950	C₂²	1	2	yes	—
28	#15689117	C₂²	1	2	yes	—
29	#15689091	C₂²	1	2	yes	—
30	#15689086	C₂²	1	2	yes	—
31	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₄₇	—	2	4	no	—
35	#15688887	C₂²	1	2	yes	—
36	#15688882	C₂²	1	2	yes	—
37	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#427	C₂²	1	1	yes	characteristic
39	C₄₇×#405	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#339	C₂²	1	2	yes	—
42	C₂×#10625350	C₂³	1	2	yes	—
43	C₂²×C₄×D₄₇	—	2	1	no	—
44	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
45	#13094046	—	2	2	no	—
46	#13094046	—	2	2	no	—
47	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×#10625325	C₂×C₄	1	2	yes	complemented
49	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic, complemented
50	#13094030	—	2	4	no	—
51	#13094030	—	2	4	no	—
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂×#10625324	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₄₇	—	2	2	no	—
57	C₂×C₈×D₄₇	—	2	2	no	—
58	C₂×C₈×D₄₇	—	2	2	no	—
59	C₂×C₈×D₄₇	—	2	2	no	—
60	C₂×C₈×D₄₇	—	2	2	no	—
61	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₄₇	D₄	1	2	yes	—
64	C₂×C₈×D₄₇	D₄	1	2	yes	—
65	#13094008	—	2	2	no	—
66	#13094004	C₂×C₄	1	4	yes	—
67	#13093999	C₂×C₄	1	4	yes	—
68	#13093994	—	2	2	no	—
69	C₄×D₁₈₈	—	2	4	no	—
70	C₂×C₄×Dic₄₇	—	2	1	no	—
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₄²×D₄₇	—	2	2	no	—
73	C₄²×D₄₇	—	2	2	no	—
74	#13093960	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
76	#13093952	—	2	4	no	—
77	#13093950	—	2	4	no	—
78	#13093947	C₂×C₄	1	4	yes	complemented
79	#13093944	C₂×C₄	1	4	yes	complemented
80	(C₂×D₄₇)⋊C₈	—	2	4	no	—
81	(C₂×D₄₇)⋊C₈	—	2	4	no	—
82	C₄×C₄₇⋊C₈	—	2	2	no	—
83	C₈×Dic₄₇	—	2	2	no	—
84	C₈×Dic₄₇	—	2	2	no	—
85	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	#117×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#108×C₄₇	—	2	2	no	—
91	#107×C₄₇	C₂×C₄	1	2	yes	complemented
92	#106×C₄₇	C₂×C₄	1	2	yes	complemented
93	#97×C₄₇	—	2	2	no	—
94	C₄×C₈×C₄₇	—	2	2	no	—
95	C₄×C₈×C₄₇	D₄	1	4	yes	complemented
96	C₂³×D₄₇	#41	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₂×C₂²⋊D₄₇	—	2	2	no	—
100	C₂²×Dic₄₇	—	2	1	no	—
101	C₂²×Dic₄₇	#41	1	1	yes	characteristic
102	#10625350	—	2	2	no	—
103	#10625350	—	2	2	no	—
104	#10625350	—	2	2	no	—
105	#10625350	—	2	2	no	—
106	C₂×D₁₈₈	—	2	4	no	—
107	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₄₇	—	2	4	no	—
109	C₂×C₄×D₄₇	—	2	8	no	—
110	C₂×C₄×D₄₇	—	2	1	no	—
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×C₄×D₄₇	—	2	1	no	—
114	C₂×C₄×D₄₇	—	2	2	no	—
115	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
117	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
118	M₁₆×C₄₇	—	2	2	no	—
119	M₁₆×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	#41	1	2	yes	—
128	C₂×C₈×C₄₇	#41	1	2	yes	—
129	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
130	C₂²⋊C₄×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	(C₂×D₄₇)⋊C₄	—	2	4	no	—
135	(C₂×D₄₇)⋊C₄	—	2	4	no	—
136	C₄⋊Dic₄₇	—	2	4	no	—
137	C₄×Dic₄₇	—	2	4	no	—
138	C₄×Dic₄₇	—	2	1	no	—
139	C₄×Dic₄₇	#41	1	2	yes	—
140	#10625329	—	2	2	no	—
141	#10625329	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
149	Dic₁₈₈	—	2	2	no	—
150	D₃₇₆	—	2	2	no	—
151	#10625325	—	2	4	no	—
152	#10625324	—	4	4	no	—
153	C₈×D₄₇	—	2	4	no	—
154	C₈×D₄₇	—	2	4	no	—
155	C₈×D₄₇	—	2	4	no	—
156	C₈×D₄₇	—	2	4	no	—
157	C₈×D₄₇	—	4	4	no	—
158	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	2	4	no	—
162	C₂²×D₄₇	—	2	2	no	—
163	C₂²×D₄₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₄₇	—	4	2	no	—
174	C₂²⋊D₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
181	D₁₈₈	—	2	2	no	—
182	D₁₈₈	—	2	2	no	—
183	D₁₈₈	—	4	8	no	—
184	C₄×D₄₇	—	2	16	no	—
185	C₄×D₄₇	—	2	2	no	—
186	C₄×D₄₇	—	2	2	no	—
187	C₄×D₄₇	—	2	2	no	—
188	C₄×D₄₇	—	2	2	no	—
189	C₄×D₄₇	—	4	2	no	—
190	C₄×D₄₇	—	4	2	no	—
191	Dic₉₄	—	2	2	no	—
192	Dic₉₄	—	2	2	no	—
193	C₈×C₄₇	—	4	2	no	—
194	C₈×C₄₇	C₄×D₄	1	2	yes	—
195	C₈×C₄₇	C₄×D₄	1	2	yes	—
196	C₈×C₄₇	#121	1	2	yes	—
197	C₈×C₄₇	#121	1	2	yes	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	#21544	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	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	C₂×D₄₇	—	2	4	no	—
207	C₂×D₄₇	—	2	4	no	—
208	C₂×D₄₇	—	2	2	no	—
209	C₂×D₄₇	—	2	2	no	—
210	C₂×D₄₇	—	4	4	no	—
211	C₂×D₄₇	—	4	2	no	—
212	C₂×D₄₇	#443	1	4	yes	complemented
213	C₄×C₄₇	—	2	4	no	—
214	C₄×C₄₇	—	4	4	no	—
215	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
217	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
218	C₄×C₄₇	#532	1	1	yes	characteristic
219	Dic₄₇	—	2	4	no	—
220	Dic₄₇	—	2	2	no	—
221	Dic₄₇	—	4	2	no	—
222	#3050	—	47	1	no	—
223	C₂×#443	—	47	1	no	—
224	#2929	—	47	2	no	—
225	C₂²×C₄×C₈	—	47	1	no	—
226	#1974	—	47	1	no	—
227	#1945	—	47	1	no	—
228	#1937	—	47	2	no	—
229	#1896	—	47	2	no	—
230	#1810	—	47	1	no	—
231	#1772	D₄₇	1	1	yes	characteristic, complemented
232	#1764	—	47	2	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	2	1	no	—
235	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
236	C₂×C₄₇	C₂×#443	1	2	yes	—
237	D₄₇	—	2	4	no	—
238	D₄₇	—	8	2	no	—
239	C₂×#135	—	47	1	no	—
240	C₂×#131	—	47	2	no	—
241	C₂³×C₈	—	47	1	no	—
242	C₂³×C₈	—	47	1	no	—
243	#525	—	47	2	no	—
244	C₂²×C₄²	—	47	1	no	—
245	#467	—	47	2	no	—
246	#466	—	47	2	no	—
247	#465	—	47	4	no	—
248	#443	—	94	4	no	—
249	#435	—	94	4	no	—
250	C₈×D₄	—	94	4	no	—
251	C₂×#108	—	47	1	no	—
252	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
253	#427	C₂×D₄₇	1	1	yes	characteristic
254	#424	—	47	2	no	—
255	C₂×#104	—	47	2	no	—
256	C₂×#104	—	47	2	no	—
257	#416	—	47	2	no	—
258	#408	—	47	2	no	—
259	#407	—	47	2	no	—
260	#405	C₂×D₄₇	1	2	yes	—
261	C₂×C₄×C₈	—	47	1	no	—
262	C₂×C₄×C₈	—	47	1	no	—
263	C₂×C₄×C₈	—	47	1	no	—
264	C₂×C₄×C₈	—	94	4	no	—
265	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
266	#341	—	47	2	no	—
267	#339	—	47	2	no	—
268	#339	C₂×D₄₇	1	2	yes	—
269	C₄₇	#21544	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	—	47	2	no	—
271	C₂³×C₄	—	47	1	no	—
272	C₂³×C₄	—	94	1	no	—
273	#135	—	94	2	no	—
274	#135	—	94	2	no	—
275	C₂×Q₁₆	—	47	1	no	—
276	C₂×SD₁₆	—	47	2	no	—
277	C₂×D₈	—	47	1	no	—
278	#131	—	94	4	no	—
279	#131	—	94	4	no	—
280	C₂×M₁₆	—	47	2	no	—
281	C₂×M₁₆	—	94	2	no	—
282	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
283	C₂²×C₈	—	47	1	no	—
284	C₂²×C₈	—	47	1	no	—
285	C₂²×C₈	—	47	2	no	—
286	C₂²×C₈	—	47	2	no	—
287	C₂²×C₈	—	47	2	no	—
288	C₂²×C₈	—	47	2	no	—
289	C₂²×C₈	—	94	2	no	—
290	C₂²×C₈	—	94	2	no	—
291	C₂²×C₈	—	94	2	no	—
292	C₂²×C₈	—	94	2	no	—
293	C₂²×C₈	—	94	2	no	—
294	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
295	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
296	#123	—	94	2	no	—
297	C₂²⋊Q₈	—	47	4	no	—
298	#121	—	47	4	no	—
299	#120	—	94	2	no	—
300	C₄×D₄	—	94	4	no	—
301	#117	C₂²×D₄₇	1	2	yes	—
302	C₂×C₄²	—	47	1	no	—
303	C₂×C₄²	—	94	2	no	—
304	C₂×C₄²	—	94	1	no	—
305	C₂×C₄²	—	94	2	no	—
306	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
307	#108	—	2	2	no	—
308	#108	—	94	2	no	—
309	#107	C₄×D₄₇	1	2	yes	complemented
310	#106	C₄×D₄₇	1	2	yes	complemented
311	C₄⋊C₈	—	94	4	no	—
312	#104	—	94	4	no	—
313	#104	—	94	4	no	—
314	#103	—	47	4	no	—
315	#102	—	47	4	no	—
316	C₂²⋊C₈	—	94	4	no	—
317	C₂²⋊C₈	—	94	4	no	—
318	#97	—	2	2	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	94	2	no	—
321	C₄×C₈	—	94	2	no	—
322	C₄×C₈	—	94	2	no	—
323	C₄×C₈	D₁₈₈	1	4	yes	complemented
324	C₂⁴	—	47	1	no	—
325	#41	—	94	2	no	—
326	#41	—	94	2	no	—
327	#41	—	94	2	no	—
328	#41	—	94	2	no	—
329	C₂×Q₈	—	47	2	no	—
330	C₂×D₄	—	47	2	no	—
331	C₂×D₄	—	94	4	no	—
332	C₂×D₄	—	94	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	47	1	no	—
335	C₂²×C₄	—	47	2	no	—
336	C₂²×C₄	—	47	2	no	—
337	C₂²×C₄	—	94	4	no	—
338	C₂²×C₄	—	94	8	no	—
339	C₂²×C₄	—	94	1	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	94	1	no	—
344	C₂²×C₄	—	94	2	no	—
345	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
346	Q₁₆	—	94	2	no	—
347	SD₁₆	—	94	4	no	—
348	D₈	—	94	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	94	2	no	—
352	M₁₆	—	94	2	no	—
353	M₁₆	—	188	4	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	47	2	no	—
356	C₂×C₈	—	47	2	no	—
357	C₂×C₈	—	94	1	no	—
358	C₂×C₈	—	94	1	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	4	no	—
362	C₂×C₈	—	94	4	no	—
363	C₂×C₈	—	94	4	no	—
364	C₂×C₈	—	94	4	no	—
365	C₂×C₈	—	94	2	no	—
366	C₂×C₈	—	188	4	no	—
367	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
370	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
371	C₂×C₈	#10625350	1	2	yes	—
372	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
373	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
374	C₂×C₈	#10625354	1	2	yes	—
375	C₄⋊C₄	—	94	4	no	—
376	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	94	4	no	—
379	C₂²⋊C₄	—	94	4	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	47	2	no	—
383	C₄²	—	94	4	no	—
384	C₄²	—	94	1	no	—
385	C₄²	C₂×D₁₈₈	1	2	yes	—
386	C₂³	—	47	2	no	—
387	C₂³	—	94	4	no	—
388	C₂³	—	94	1	no	—
389	C₂³	—	94	1	no	—
390	C₂³	—	94	2	no	—
391	C₂³	#41×D₄₇	1	1	yes	characteristic
392	Q₈	—	94	2	no	—
393	Q₈	—	94	2	no	—
394	D₄	—	94	2	no	—
395	D₄	—	94	2	no	—
396	D₄	—	188	8	no	—
397	D₄	—	188	2	no	—
398	D₄	—	188	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	47	2	no	—
403	C₂×C₄	—	94	16	no	—
404	C₂×C₄	—	94	4	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	1	no	—
407	C₂×C₄	—	94	1	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	188	2	no	—
414	C₂×C₄	—	188	2	no	—
415	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
418	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
420	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
421	C₈	—	4	2	no	—
422	C₈	—	94	2	no	—
423	C₈	—	94	2	no	—
424	C₈	—	188	2	no	—
425	C₈	C₄×D₁₈₈	1	2	yes	—
426	C₈	C₄×D₁₈₈	1	2	yes	—
427	C₈	#13093999	1	2	yes	—
428	C₈	#13093999	1	2	yes	—
429	C₂²	—	2	2	no	—
430	C₂²	—	47	4	no	—
431	C₂²	—	94	4	no	—
432	C₂²	—	94	4	no	—
433	C₂²	—	94	2	no	—
434	C₂²	—	94	2	no	—
435	C₂²	—	188	4	no	—
436	C₂²	—	188	2	no	—
437	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
438	C₂²	#15689635	1	1	yes	characteristic
439	C₂²	#15689660	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	4	4	no	—
442	C₄	—	94	4	no	—
443	C₄	—	94	2	no	—
444	C₄	—	188	2	no	—
445	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
446	C₄	C₄×#10625354	1	1	yes	characteristic
447	C₄	C₂×#13093999	1	1	yes	characteristic
448	C₄	#15689670	1	1	yes	characteristic
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	94	4	no	—
452	C₂	—	376	2	no	—
453	C₂	C₄×#13093999	1	1	yes	characteristic
454	C₂	#443×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1772	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252970	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1772	D₄₇
hypocenter	C₄₇	#21544
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
2. C₂×#15689241	C₂	semidirect
3. #20252084	C₂	semidirect
4. C₂×C₄×C₈×D₄₇	C₂	semidirect
5. #20244274	C₂	semidirect
6. #20244137	C₂	semidirect
7. #20244093	C₂	semidirect
8. #20243830	C₂	semidirect
9. #20243423	C₂	semidirect
10. #20243227	C₂	semidirect
11. C₄₇×#1772	C₂	semidirect
18. #15689365	C₄	semidirect
19. #15689360	C₄	semidirect
20. #15689353	C₄	semidirect
47. C₂×Dic₁₈₈	C₂×C₄	semidirect
48. C₂×#10625325	C₂×C₄	semidirect
49. C₂×D₃₇₆	C₂×C₄	semidirect
78. #13093947	C₂×C₄	semidirect
79. #13093944	C₂×C₄	semidirect
91. #107×C₄₇	C₂×C₄	semidirect
92. #106×C₄₇	C₂×C₄	semidirect
95. C₄×C₈×C₄₇	D₄	semidirect
212. C₂×D₄₇	#443	semidirect
231. #1772	D₄₇	semidirect
269. C₄₇	#21544	semidirect
309. #107	C₄×D₄₇	semidirect
310. #106	C₄×D₄₇	semidirect
323. C₄×C₈	D₁₈₈	semidirect

Maximal subgroups

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

subgroup	index
#20252970	2
C₂×#15689241	2
#20252084	2
C₂×C₄×C₈×D₄₇	2
#20244274	2
#20244137	2
#20244093	2
#20243830	2
#20243423	2
#20243227	2
C₄₇×#1772	2
#21544	47