Subgroups — #26234802

Order 12032.

808 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	#20252301	C₂	1	2	yes	maximal
2	C₂×#15689243	C₂	1	1	yes	maximal, characteristic
3	#20251999	C₂	1	1	yes	maximal, characteristic, complemented
4	#20251996	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244177	C₂	1	2	yes	maximal, complemented
6	#20243631	C₂	1	2	yes	maximal, complemented
7	#20243626	C₂	1	2	yes	maximal, complemented
8	#20243561	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243439	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243274	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1814	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	C₂²	1	1	yes	characteristic
13	#15689890	C₂²	1	2	yes	—
14	#15689889	C₂²	1	2	yes	—
15	C₂×#13094030	C₂²	1	1	yes	characteristic
16	#15689243	C₄	1	4	yes	complemented
17	#15689243	C₄	1	4	yes	complemented
18	#15689242	—	2	4	no	—
19	#15689237	—	2	4	no	—
20	#15689172	—	2	2	no	—
21	#15689172	C₂²	1	2	yes	—
22	#15689171	C₂²	1	2	yes	—
23	#15689170	—	2	2	no	—
24	C₂×#13093960	—	2	2	no	—
25	C₂×#13093960	C₂²	1	1	yes	characteristic
26	C₂×#13093960	C₂²	1	1	yes	characteristic
27	C₂×#13093959	C₂²	1	2	yes	—
28	C₂×#13093959	C₂²	1	1	yes	characteristic
29	#108×D₄₇	—	2	2	no	—
30	#15689146	C₂²	1	2	yes	—
31	#15689141	C₂²	1	2	yes	—
32	C₂×#13093951	C₂²	1	1	yes	characteristic
33	C₂×#13093950	C₂²	1	1	yes	characteristic
34	#15689079	C₂²	1	2	yes	—
35	C₂×#13093934	C₂²	1	1	yes	characteristic
36	#15688893	C₂²	1	2	yes	—
37	#15688882	C₂²	1	2	yes	—
38	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#427	C₂²	1	1	yes	characteristic
41	C₄₇×#421	C₂²	1	2	yes	—
42	C₄₇×#344	C₂²	1	2	yes	—
43	C₂×#10625350	C₂³	1	1	yes	characteristic
44	#13094044	C₂×C₄	1	4	yes	—
45	#13094044	D₄	1	4	yes	—
46	C₂×#10625337	Q₈	1	1	yes	characteristic
47	C₂×#10625335	Q₈	1	1	yes	characteristic
48	C₂×#10625336	Q₈	1	1	yes	characteristic
49	C₂×#10625334	Q₈	1	1	yes	characteristic
50	#13094032	—	2	4	no	—
51	#13094031	—	2	4	no	—
52	#13094031	—	4	2	no	—
53	#13094030	—	2	1	no	—
54	#13094030	—	2	1	no	—
55	#13094030	—	4	2	no	—
56	#13094030	C₂×C₄	1	2	yes	—
57	#13094030	C₂×C₄	1	2	yes	—
58	C₂×#10625329	—	2	4	no	—
59	C₂×#10625329	C₂³	1	2	yes	—
60	C₂×#10625329	C₂³	1	1	yes	characteristic
61	C₂×#10625329	C₂³	1	2	yes	—
62	C₂×#10625324	—	2	1	no	—
63	M₁₆×D₄₇	—	2	4	no	—
64	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂×C₈×D₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	#13093960	—	2	1	no	—
68	#13093960	—	2	1	no	—
69	#13093960	—	2	4	no	—
70	#13093960	D₄	1	2	yes	—
71	#13093960	D₄	1	2	yes	—
72	#13093959	—	2	4	no	—
73	#13093959	—	2	2	no	—
74	#13093959	—	2	2	no	—
75	#13093959	C₂×C₄	1	4	yes	—
76	Dic₄₇⋊C₈	—	4	2	no	—
77	#13093952	—	2	4	no	—
78	#13093951	C₂×C₄	1	4	yes	—
79	#13093950	C₂×C₄	1	4	yes	—
80	#13093935	—	2	2	no	—
81	#13093934	C₂×C₄	1	2	yes	—
82	#13093934	C₂×C₄	1	2	yes	—
83	C₄×C₄₇⋊C₈	—	2	2	no	—
84	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
85	#131×C₄₇	—	2	1	no	—
86	#131×C₄₇	—	2	1	no	—
87	#131×C₄₇	C₂×C₄	1	2	yes	—
88	#131×C₄₇	C₂×C₄	1	2	yes	—
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
91	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	—	2	1	no	—
93	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	#117×C₄₇	C₂³	1	2	yes	—
95	#108×C₄₇	—	2	1	no	—
96	#108×C₄₇	—	2	1	no	—
97	#107×C₄₇	—	2	1	no	—
98	#106×C₄₇	—	2	1	no	—
99	#104×C₄₇	—	2	4	no	—
100	#41×C₄₇	—	2	1	no	—
101	#41×C₄₇	—	2	1	no	—
102	#41×C₄₇	C₂²×C₄	1	2	yes	—
103	#41×C₄₇	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
105	C₂×D₄×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂×C₂²⋊D₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	1	no	—
111	#10625350	—	2	1	no	—
112	#10625350	—	2	1	no	—
113	#10625350	C₂²×C₄	1	2	yes	—
114	#10625350	C₂×D₄	1	2	yes	—
115	C₂×D₁₈₈	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₄×D₄₇	—	2	1	no	—
117	C₂×Dic₉₄	C₂×Q₈	1	1	yes	characteristic
118	M₁₆×C₄₇	—	2	1	no	—
119	M₁₆×C₄₇	—	2	2	no	—
120	M₁₆×C₄₇	—	2	2	no	—
121	M₁₆×C₄₇	—	2	2	no	—
122	M₁₆×C₄₇	—	2	2	no	—
123	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
133	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
134	C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₂²⋊C₄×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	#10625337	C₄⋊C₄	1	4	yes	—
138	#10625336	C₄⋊C₄	1	4	yes	—
139	#10625335	C₄⋊C₄	1	4	yes	—
140	#10625334	C₄⋊C₄	1	4	yes	—
141	C₄×Dic₄₇	—	2	1	no	—
142	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
143	#10625329	—	2	1	no	—
144	#10625329	—	2	2	no	—
145	#10625329	—	2	2	no	—
146	#10625329	—	2	2	no	—
147	#10625329	—	4	4	no	—
148	#10625329	C₂²×C₄	1	2	yes	—
149	#10625329	C₂×D₄	1	4	yes	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	4	4	no	—
154	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
156	C₂×C₄₇⋊C₈	C₂×Q₈	1	1	yes	characteristic
157	C₂×C₄₇⋊C₈	C₂×Q₈	1	1	yes	characteristic
158	#10625324	—	2	2	no	—
159	#10625324	—	2	2	no	—
160	#10625324	—	4	4	no	—
161	C₈×D₄₇	—	2	2	no	—
162	C₈×D₄₇	—	2	2	no	—
163	C₈×D₄₇	—	4	4	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
166	C₂²×D₄₇	—	2	1	no	—
167	Q₈×C₄₇	—	2	1	no	—
168	Q₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
169	D₄×C₄₇	—	2	2	no	—
170	D₄×C₄₇	—	2	2	no	—
171	D₄×C₄₇	—	2	1	no	—
172	D₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂²⋊D₄₇	—	2	2	no	—
184	C₂²⋊D₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	8	1	no	—
188	D₁₈₈	—	2	1	no	—
189	D₁₈₈	C₂×C₄⋊C₄	1	2	yes	—
190	C₄×D₄₇	—	2	2	no	—
191	C₄×D₄₇	—	2	2	no	—
192	Dic₉₄	—	2	1	no	—
193	Dic₉₄	C₂×C₄⋊C₄	1	2	yes	—
194	C₈×C₄₇	—	2	2	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
197	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
198	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
199	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
200	C₄₇⋊C₈	—	2	2	no	—
201	C₄₇⋊C₈	—	2	4	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
204	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
205	#22695	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	4	1	no	—
208	C₂²×C₄₇	—	8	1	no	—
209	C₂²×C₄₇	#520	1	1	yes	characteristic
210	C₂²×C₄₇	#547	1	1	yes	characteristic
211	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
212	C₂×D₄₇	—	2	2	no	—
213	C₂×D₄₇	—	8	1	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	8	2	no	—
216	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
217	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₄₇	D₄²	1	1	yes	characteristic
219	C₄×C₄₇	#554	1	1	yes	characteristic
220	Dic₄₇	—	2	2	no	—
221	Dic₄₇	—	4	2	no	—
222	#2957	—	47	2	no	—
223	C₂×#444	—	47	1	no	—
224	#2916	—	47	1	no	—
225	#2916	—	47	1	no	—
226	#1953	—	47	2	no	—
227	#1861	—	47	2	no	—
228	#1861	—	47	2	no	—
229	#1849	—	47	1	no	—
230	#1814	—	47	1	no	—
231	#1814	D₄₇	1	1	yes	characteristic, complemented
232	#1773	—	47	1	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	2	1	no	—
235	C₂×C₄₇	—	2	1	no	—
236	C₂×C₄₇	—	4	2	no	—
237	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
238	D₄₇	—	4	2	no	—
239	C₂×#135	—	47	1	no	—
240	#568	—	47	2	no	—
241	#568	—	47	2	no	—
242	C₂×#131	—	47	1	no	—
243	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
244	#444	—	47	4	no	—
245	#444	—	47	4	no	—
246	#444	—	94	4	no	—
247	#443	—	94	4	no	—
248	#430	—	47	2	no	—
249	#430	—	47	2	no	—
250	#430	—	94	2	no	—
251	#430	—	94	2	no	—
252	C₂×#108	—	47	1	no	—
253	C₂×#108	—	47	1	no	—
254	C₂×#108	—	47	2	no	—
255	C₂×#108	—	47	1	no	—
256	C₂×#108	—	94	2	no	—
257	C₂×#108	—	94	2	no	—
258	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
259	#427	C₂×D₄₇	1	1	yes	characteristic
260	#423	—	47	2	no	—
261	#421	—	47	2	no	—
262	#421	C₂×D₄₇	1	2	yes	—
263	C₂×#104	—	47	1	no	—
264	C₂×#104	—	47	1	no	—
265	#405	—	47	2	no	—
266	C₂×#97	—	47	1	no	—
267	#344	—	47	2	no	—
268	#344	C₂×D₄₇	1	2	yes	—
269	#339	—	47	2	no	—
270	C₄₇	#22695	1	1	yes	characteristic, complemented, Sylow
271	C₂×#41	—	47	1	no	—
272	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
273	#135	—	47	4	no	—
274	#135	—	47	4	no	—
275	C₂×Q₁₆	—	47	1	no	—
276	C₂×SD₁₆	—	47	1	no	—
277	C₂×SD₁₆	—	47	1	no	—
278	C₂×D₈	—	47	1	no	—
279	#131	—	2	1	no	—
280	#131	—	2	1	no	—
281	#131	—	47	2	no	—
282	#131	—	47	2	no	—
283	#131	—	94	1	no	—
284	#131	—	94	1	no	—
285	#131	—	94	4	no	—
286	#131	—	94	4	no	—
287	#131	—	188	2	no	—
288	#131	—	188	2	no	—
289	#131	C₄×D₄₇	1	2	yes	—
290	#131	C₄×D₄₇	1	2	yes	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	47	1	no	—
293	C₂×M₁₆	—	47	2	no	—
294	C₂×M₁₆	—	47	2	no	—
295	C₂×M₁₆	—	94	1	no	—
296	C₂×M₁₆	—	94	4	no	—
297	C₂×M₁₆	—	94	4	no	—
298	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
299	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	47	1	no	—
302	C₂²×C₈	—	94	1	no	—
303	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
304	#117	C₂²×D₄₇	1	2	yes	—
305	C₂×C₄²	—	47	1	no	—
306	#108	—	2	1	no	—
307	#108	—	2	1	no	—
308	#108	—	47	4	no	—
309	#108	—	47	2	no	—
310	#108	—	47	2	no	—
311	#108	—	94	4	no	—
312	#108	—	94	2	no	—
313	#108	—	94	2	no	—
314	#108	—	94	4	no	—
315	#108	—	94	1	no	—
316	#108	—	94	1	no	—
317	#107	—	2	1	no	—
318	#106	—	2	1	no	—
319	C₄⋊C₈	—	188	2	no	—
320	#104	—	2	4	no	—
321	#104	—	47	4	no	—
322	#104	—	47	4	no	—
323	#104	—	94	4	no	—
324	#97	—	47	2	no	—
325	#97	—	47	2	no	—
326	#97	—	94	2	no	—
327	C₄×C₈	—	94	2	no	—
328	#41	—	2	1	no	—
329	#41	—	2	1	no	—
330	#41	—	47	2	no	—
331	#41	—	47	2	no	—
332	#41	—	94	1	no	—
333	#41	—	94	1	no	—
334	#41	C₂×C₄×D₄₇	1	2	yes	—
335	#41	D₄×D₄₇	1	2	yes	—
336	C₂×Q₈	—	47	1	no	—
337	C₂×Q₈	Q₈×D₄₇	1	1	yes	characteristic
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	47	1	no	—
340	C₂×D₄	—	94	1	no	—
341	C₂×D₄	Q₈×D₄₇	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	94	1	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
346	Q₁₆	—	47	4	no	—
347	SD₁₆	—	47	4	no	—
348	SD₁₆	—	47	4	no	—
349	D₈	—	47	4	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	47	2	no	—
356	M₁₆	—	47	4	no	—
357	M₁₆	—	94	1	no	—
358	M₁₆	—	94	2	no	—
359	M₁₆	—	94	2	no	—
360	M₁₆	—	94	2	no	—
361	M₁₆	—	94	2	no	—
362	M₁₆	—	94	2	no	—
363	M₁₆	—	188	4	no	—
364	M₁₆	—	188	4	no	—
365	M₁₆	C₂×C₄×D₄₇	1	2	yes	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	47	2	no	—
371	C₂×C₈	—	47	2	no	—
372	C₂×C₈	—	47	1	no	—
373	C₂×C₈	—	47	1	no	—
374	C₂×C₈	—	94	2	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	2	no	—
377	C₂×C₈	—	94	2	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	188	4	no	—
380	C₂×C₈	—	188	4	no	—
381	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
383	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
384	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
385	C₂×C₈	#10625352	1	1	yes	characteristic
386	C₂×C₈	#10625352	1	1	yes	characteristic
387	C₄⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	47	2	no	—
391	C₄²	—	94	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	94	1	no	—
394	C₂³	#13094071	1	1	yes	characteristic
395	Q₈	—	2	1	no	—
396	Q₈	—	47	2	no	—
397	Q₈	—	94	1	no	—
398	Q₈	C₄⋊C₄×D₄₇	1	2	yes	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	1	no	—
402	D₄	—	47	2	no	—
403	D₄	—	94	2	no	—
404	D₄	—	94	2	no	—
405	D₄	—	94	1	no	—
406	D₄	C₄⋊C₄×D₄₇	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	94	1	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	376	1	no	—
416	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
420	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
421	C₂×C₄	#13094070	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	47	2	no	—
425	C₈	—	47	2	no	—
426	C₈	—	94	4	no	—
427	C₈	—	94	2	no	—
428	C₈	—	188	2	no	—
429	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
430	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
431	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
432	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	94	2	no	—
437	C₂²	—	376	1	no	—
438	C₂²	#15689603	1	1	yes	characteristic
439	C₂²	#15689773	1	1	yes	characteristic
440	C₂²	#15689786	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	8	2	no	—
443	C₄	—	94	2	no	—
444	C₄	—	188	2	no	—
445	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
446	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
447	C₄	#15689757	1	1	yes	characteristic
448	C₄	#15689831	1	1	yes	characteristic
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	4	2	no	—
453	C₂	—	188	2	no	—
454	C₂	#20246284	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689757
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1814	C₂
socle	C₂×C₄₇	D₄×C₄⋊C₄
prime radical	C₂×#13094044	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1814	D₄₇
hypocenter	C₄₇	#22695
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1814

Complements

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

N	H ≅ G/N	type
3. #20251999	C₂	semidirect
4. #20251996	C₂	semidirect
5. #20244177	C₂	semidirect
6. #20243631	C₂	semidirect
7. #20243626	C₂	semidirect
8. #20243561	C₂	semidirect
9. #20243439	C₂	semidirect
10. #20243274	C₂	semidirect
11. C₄₇×#1814	C₂	semidirect
16. #15689243	C₄	semidirect
17. #15689243	C₄	semidirect
231. #1814	D₄₇	semidirect
270. C₄₇	#22695	semidirect

Maximal subgroups

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

subgroup	index
#20252301	2
C₂×#15689243	2
#20251999	2
#20251996	2
#20244177	2
#20243631	2
#20243626	2
#20243561	2
#20243439	2
#20243274	2
C₄₇×#1814	2
#22695	47