Subgroups — #28602620

Order 15104.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434582	C₂	1	1	yes	maximal, characteristic
2	#21433014	C₂	1	1	yes	maximal, characteristic, complemented
3	#21432949	C₂	1	1	yes	maximal, characteristic, complemented
4	#21425006	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424994	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424627	C₂	1	2	yes	maximal, complemented
7	#21424622	C₂	1	2	yes	maximal, complemented
8	#21424584	C₂	1	2	yes	maximal, complemented
9	#21424577	C₂	1	2	yes	maximal, complemented
10	#21424220	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273755	C₂²	1	2	yes	—
13	C₂×#14273749	C₂²	1	1	yes	characteristic
14	C₂²×D₄₇₂	C₂²	1	1	yes	characteristic
15	#16838168	C₂²	1	2	yes	—
16	#16837971	C₂²	1	2	yes	—
17	#16837876	C₂²	1	2	yes	—
18	#16837791	C₄	1	4	yes	complemented
19	#16837786	C₄	1	2	yes	complemented
20	#16837779	C₄	1	2	yes	complemented
21	#16837525	—	2	2	no	—
22	#16837520	—	2	2	no	—
23	#16837515	—	2	2	no	—
24	C₄×D₄₇₂	—	2	2	no	—
25	C₂×#14273663	C₂²	1	1	yes	characteristic
26	#16837440	C₂²	1	1	yes	characteristic
27	#16837420	C₂²	1	2	yes	—
28	#16837418	C₂²	1	2	yes	—
29	#16837408	C₂²	1	2	yes	—
30	#16837406	C₂²	1	2	yes	—
31	C₂×#14273643	C₂²	1	2	yes	—
32	#16837375	C₂²	1	2	yes	—
33	#16837173	C₂²	1	2	yes	—
34	#16837158	C₂²	1	2	yes	—
35	C₅₉×#405	C₂²	1	1	yes	characteristic
36	C₅₉×#405	C₂²	1	1	yes	characteristic
37	C₅₉×#405	C₂²	1	1	yes	characteristic
38	C₅₉×#338	C₂²	1	1	yes	characteristic
39	C₅₉×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
40	C₅₉×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
41	C₅₉×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
42	C₂×#11745685	C₂³	1	2	yes	—
43	C₂²×D₂₃₆	C₂³	1	2	yes	—
44	#14273755	—	4	2	no	—
45	#14273755	—	4	2	no	—
46	#14273749	—	2	1	no	—
47	#14273749	—	2	1	no	—
48	#14273749	—	2	1	no	—
49	#14273749	—	2	1	no	—
50	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#11745660	C₂×C₄	1	2	yes	complemented
52	C₂×#11745660	C₂×C₄	1	4	yes	complemented
53	C₂×D₄₇₂	—	2	1	no	—
54	C₂×D₄₇₂	—	2	1	no	—
55	C₂×D₄₇₂	—	2	1	no	—
56	C₂×D₄₇₂	—	2	1	no	—
57	C₂×D₄₇₂	C₂×C₄	1	2	yes	—
58	C₂×D₄₇₂	C₂×C₄	1	2	yes	—
59	C₂×D₄₇₂	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×D₄₇₂	C₂×C₄	1	4	yes	complemented
61	#14273735	—	4	2	no	—
62	#14273733	—	2	4	no	—
63	C₂×#11745664	C₂³	1	2	yes	—
64	M₁₆×D₅₉	—	4	2	no	—
65	#14273724	C₂×C₄	1	4	yes	complemented
66	#14273715	C₂×C₄	1	4	yes	complemented
67	#14273702	—	4	2	no	—
68	#14273697	—	4	2	no	—
69	C₄×D₂₃₆	—	2	4	no	—
70	#14273689	—	4	2	no	—
71	#14273686	C₂³	1	2	yes	—
72	C₂²⋊C₄×D₅₉	—	4	2	no	—
73	#14273663	—	2	1	no	—
74	#14273663	—	2	1	no	—
75	#14273661	—	2	1	no	—
76	#14273659	—	2	1	no	—
77	#14273655	—	2	4	no	—
78	#14273653	—	4	2	no	—
79	#14273649	—	2	4	no	—
80	#14273647	—	4	2	no	—
81	#14273643	—	4	2	no	—
82	#14273641	—	4	2	no	—
83	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
87	#117×C₅₉	C₂³	1	1	yes	characteristic
88	#117×C₅₉	C₂³	1	1	yes	characteristic
89	#117×C₅₉	C₂³	1	1	yes	characteristic
90	#97×C₅₉	—	2	1	no	—
91	#97×C₅₉	C₂×C₄	1	2	yes	complemented
92	#97×C₅₉	D₄	1	2	yes	complemented
93	C₄×C₈×C₅₉	—	2	1	no	—
94	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₅₉	D₄	1	2	yes	complemented
96	C₂³×D₅₉	—	2	2	no	—
97	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
98	C₂×C₂²⋊D₅₉	—	2	2	no	—
99	#11745685	—	2	2	no	—
100	#11745685	—	2	2	no	—
101	#11745685	—	2	2	no	—
102	#11745685	—	2	2	no	—
103	C₂×D₂₃₆	—	2	2	no	—
104	C₂×D₂₃₆	—	2	2	no	—
105	C₂×D₂₃₆	—	2	2	no	—
106	C₂×D₂₃₆	—	2	2	no	—
107	C₂×D₂₃₆	—	2	2	no	—
108	C₂×D₂₃₆	—	4	4	no	—
109	C₂×D₂₃₆	C₂²×C₄	1	4	yes	—
110	C₂×D₂₃₆	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₅₉	—	2	2	no	—
112	C₂×C₄×D₅₉	—	4	4	no	—
113	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
114	M₁₆×C₅₉	—	2	1	no	—
115	M₁₆×C₅₉	—	2	1	no	—
116	M₁₆×C₅₉	—	2	1	no	—
117	M₁₆×C₅₉	—	2	1	no	—
118	M₁₆×C₅₉	—	2	1	no	—
119	M₁₆×C₅₉	—	2	1	no	—
120	C₂×C₈×C₅₉	—	2	1	no	—
121	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
128	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
129	C₄⋊C₄×C₅₉	—	2	1	no	—
130	C₄⋊C₄×C₅₉	—	2	1	no	—
131	C₄⋊C₄×C₅₉	—	2	1	no	—
132	C₂²⋊C₄×C₅₉	—	2	1	no	—
133	C₂²⋊C₄×C₅₉	—	2	1	no	—
134	C₂²⋊C₄×C₅₉	—	2	1	no	—
135	C₄²×C₅₉	—	2	1	no	—
136	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
137	C₄²×C₅₉	C₂×D₄	1	2	yes	—
138	C₂²⋊Dic₅₉	—	2	2	no	—
139	(C₂×D₅₉)⋊C₄	—	4	4	no	—
140	(C₂×D₅₉)⋊C₄	—	4	4	no	—
141	C₄⋊Dic₅₉	—	2	2	no	—
142	C₄×Dic₅₉	—	2	2	no	—
143	#11745664	—	2	2	no	—
144	#11745664	—	2	2	no	—
145	C₂×C₅₉⋊C₈	—	2	2	no	—
146	Dic₂₃₆	—	2	1	no	—
147	Dic₂₃₆	—	2	1	no	—
148	D₄₇₂	—	2	2	no	—
149	D₄₇₂	—	2	2	no	—
150	D₄₇₂	—	2	2	no	—
151	D₄₇₂	—	2	2	no	—
152	D₄₇₂	—	2	1	no	—
153	D₄₇₂	—	2	1	no	—
154	D₄₇₂	—	4	4	no	—
155	#11745660	—	2	2	no	—
156	#11745660	—	2	2	no	—
157	#11745660	—	4	4	no	—
158	#11745659	—	4	4	no	—
159	C₈×D₅₉	—	4	4	no	—
160	C₂³×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₅₉	—	2	4	no	—
162	C₂²×D₅₉	—	2	2	no	—
163	C₂²×D₅₉	—	4	2	no	—
164	C₂²×D₅₉	—	4	2	no	—
165	C₂²×D₅₉	—	16	2	no	—
166	C₂×C₄×C₅₉	—	2	2	no	—
167	C₂×C₄×C₅₉	—	2	2	no	—
168	C₂×C₄×C₅₉	—	4	1	no	—
169	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²⋊D₅₉	—	4	2	no	—
176	C₂²⋊D₅₉	—	4	2	no	—
177	C₂×Dic₅₉	—	2	2	no	—
178	C₂×Dic₅₉	—	4	2	no	—
179	D₂₃₆	—	2	2	no	—
180	D₂₃₆	—	2	4	no	—
181	D₂₃₆	—	2	4	no	—
182	D₂₃₆	—	2	2	no	—
183	D₂₃₆	—	4	2	no	—
184	D₂₃₆	—	4	2	no	—
185	D₂₃₆	—	16	4	no	—
186	C₄×D₅₉	—	4	2	no	—
187	C₄×D₅₉	—	4	2	no	—
188	C₄×D₅₉	—	16	4	no	—
189	Dic₁₁₈	—	2	2	no	—
190	Dic₁₁₈	—	2	2	no	—
191	C₈×C₅₉	—	2	2	no	—
192	C₈×C₅₉	—	2	2	no	—
193	C₈×C₅₉	—	4	1	no	—
194	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
195	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
196	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
197	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
198	C₅₉⋊C₈	—	4	2	no	—
199	#22286	—	59	1	no	maximal, Sylow
200	C₂²×C₅₉	—	4	1	no	—
201	C₂²×C₅₉	#518	1	1	yes	characteristic
202	C₂²×C₅₉	#535	1	1	yes	characteristic
203	C₂²×C₅₉	#540	1	1	yes	characteristic
204	C₂×D₅₉	—	4	2	no	—
205	C₂×D₅₉	—	4	4	no	—
206	C₂×D₅₉	—	8	4	no	—
207	C₂×D₅₉	—	8	2	no	—
208	C₂×D₅₉	—	8	4	no	—
209	C₂×D₅₉	—	16	2	no	—
210	C₄×C₅₉	—	4	2	no	—
211	C₄×C₅₉	—	4	2	no	—
212	C₄×C₅₉	—	8	1	no	—
213	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₅₉	#518	1	1	yes	characteristic
215	C₄×C₅₉	#535	1	1	yes	characteristic
216	C₄×C₅₉	#540	1	1	yes	characteristic
217	Dic₅₉	—	4	2	no	—
218	Dic₅₉	—	8	2	no	—
219	#3155	—	59	1	no	—
220	#2957	—	59	1	no	—
221	#2948	—	59	1	no	—
222	#1978	—	59	1	no	—
223	#1976	—	59	1	no	—
224	#1911	—	59	2	no	—
225	#1910	—	59	2	no	—
226	#1904	—	59	2	no	—
227	#1903	—	59	2	no	—
228	#1833	—	59	1	no	—
229	#1747	D₅₉	1	1	yes	characteristic, complemented
230	C₂×C₅₉	—	2	1	no	—
231	C₂×C₅₉	—	2	1	no	—
232	C₂×C₅₉	—	2	1	no	—
233	C₂×C₅₉	#2328	1	1	yes	characteristic
234	D₅₉	—	8	2	no	—
235	D₅₉	—	8	4	no	—
236	C₂×AGL(1,ℤ/8)	—	59	2	no	—
237	C₂×#135	—	59	1	no	—
238	C₂²×D₈	—	59	1	no	—
239	#568	—	59	2	no	—
240	#535	—	59	2	no	—
241	#518	—	59	2	no	—
242	#496	—	59	4	no	—
243	#495	—	59	2	no	—
244	#493	—	59	2	no	—
245	#444	—	118	2	no	—
246	#443	—	118	2	no	—
247	#442	—	118	2	no	—
248	C₄×D₈	—	118	2	no	—
249	C₂×#108	—	59	1	no	—
250	#427	—	59	1	no	—
251	#421	—	59	2	no	—
252	#421	—	59	2	no	—
253	#418	—	59	2	no	—
254	#418	—	59	2	no	—
255	C₂×#100	—	59	2	no	—
256	#410	—	59	2	no	—
257	#405	C₂×D₅₉	1	1	yes	characteristic
258	#405	C₂×D₅₉	1	1	yes	characteristic
259	#405	C₂×D₅₉	1	1	yes	characteristic
260	#344	—	59	2	no	—
261	#338	C₂×D₅₉	1	1	yes	characteristic
262	H(3,ℤ/4)	—	59	2	no	—
263	H(3,ℤ/4)	C₂×D₅₉	1	1	yes	characteristic
264	H(3,ℤ/4)	C₂×D₅₉	1	1	yes	characteristic
265	H(3,ℤ/4)	C₂×D₅₉	1	1	yes	characteristic
266	C₅₉	#22286	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	59	2	no	—
268	C₂²×D₄	—	59	2	no	—
269	AGL(1,ℤ/8)	—	236	2	no	—
270	AGL(1,ℤ/8)	—	236	2	no	—
271	#135	—	118	1	no	—
272	#135	—	118	1	no	—
273	#135	—	118	1	no	—
274	#135	—	118	1	no	—
275	C₂×Q₁₆	—	59	1	no	—
276	C₂×SD₁₆	—	59	2	no	—
277	C₂×SD₁₆	—	59	4	no	—
278	C₂×D₈	—	59	2	no	—
279	C₂×D₈	—	59	2	no	—
280	C₂×D₈	—	59	1	no	—
281	C₂×D₈	—	59	4	no	—
282	C₂×D₈	—	118	1	no	—
283	C₂×D₈	—	118	1	no	—
284	C₂×D₈	—	118	1	no	—
285	C₂×D₈	—	118	1	no	—
286	#131	—	118	4	no	—
287	#131	—	236	2	no	—
288	C₂×M₁₆	—	59	2	no	—
289	C₂×M₁₆	—	236	2	no	—
290	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
291	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
292	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
294	#127	—	59	4	no	—
295	#124	—	59	4	no	—
296	#121	—	236	2	no	—
297	#120	—	236	2	no	—
298	C₄×D₄	—	118	4	no	—
299	C₄×D₄	—	236	2	no	—
300	#117	—	59	2	no	—
301	#117	C₂²×D₅₉	1	1	yes	characteristic
302	#117	C₂²×D₅₉	1	1	yes	characteristic
303	#117	C₂²×D₅₉	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	236	2	no	—
305	#108	—	118	1	no	—
306	#108	—	118	1	no	—
307	#107	—	118	1	no	—
308	#106	—	118	1	no	—
309	#104	—	118	4	no	—
310	#104	—	236	2	no	—
311	#102	—	118	4	no	—
312	#102	—	236	2	no	—
313	#100	—	236	2	no	—
314	#99	—	236	2	no	—
315	#97	—	2	1	no	—
316	#97	C₄×D₅₉	1	2	yes	complemented
317	#97	D₂₃₆	1	2	yes	complemented
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	C₄×D₅₉	1	2	yes	complemented
320	C₄×C₈	D₂₃₆	1	2	yes	complemented
321	C₂⁴	—	118	2	no	—
322	#41	—	118	2	no	—
323	#41	—	118	2	no	—
324	#41	—	118	2	no	—
325	#41	—	118	2	no	—
326	C₂×Q₈	—	59	2	no	—
327	C₂×D₄	—	59	4	no	—
328	C₂×D₄	—	59	2	no	—
329	C₂×D₄	—	118	2	no	—
330	C₂×D₄	—	118	2	no	—
331	C₂×D₄	—	118	2	no	—
332	C₂×D₄	—	118	2	no	—
333	C₂×D₄	—	118	2	no	—
334	C₂×D₄	—	118	2	no	—
335	C₂×D₄	—	236	4	no	—
336	C₂²×C₄	—	118	2	no	—
337	C₂²×C₄	—	236	4	no	—
338	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
339	Q₁₆	—	118	1	no	—
340	Q₁₆	—	118	1	no	—
341	SD₁₆	—	118	2	no	—
342	SD₁₆	—	118	2	no	—
343	SD₁₆	—	236	4	no	—
344	D₈	—	118	2	no	—
345	D₈	—	118	2	no	—
346	D₈	—	118	2	no	—
347	D₈	—	118	2	no	—
348	D₈	—	118	1	no	—
349	D₈	—	118	1	no	—
350	D₈	—	236	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	118	2	no	—
358	M₁₆	—	118	2	no	—
359	M₁₆	—	236	4	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	118	2	no	—
362	C₂×C₈	—	236	4	no	—
363	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
364	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
366	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
367	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
368	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
369	C₂×C₈	#11745685	1	1	yes	characteristic
370	C₂×C₈	#11745685	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	118	2	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	118	2	no	—
379	C₂²⋊C₄	—	236	4	no	—
380	C₂²⋊C₄	—	236	4	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	118	2	no	—
383	C₄²	C₂×C₄×D₅₉	1	2	yes	—
384	C₄²	C₂×D₂₃₆	1	2	yes	—
385	C₂³	—	118	4	no	—
386	C₂³	—	118	2	no	—
387	C₂³	—	944	2	no	—
388	C₂³	—	236	2	no	—
389	C₂³	—	236	2	no	—
390	C₂³	#14273773	1	1	yes	characteristic
391	Q₈	—	118	2	no	—
392	Q₈	—	118	2	no	—
393	D₄	—	118	4	no	—
394	D₄	—	118	2	no	—
395	D₄	—	118	2	no	—
396	D₄	—	118	4	no	—
397	D₄	—	944	4	no	—
398	D₄	—	236	2	no	—
399	D₄	—	236	2	no	—
400	D₄	—	236	2	no	—
401	D₄	—	236	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	118	2	no	—
406	C₂×C₄	—	944	4	no	—
407	C₂×C₄	—	236	2	no	—
408	C₂×C₄	—	236	2	no	—
409	C₂×C₄	—	236	2	no	—
410	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
412	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
413	C₂×C₄	#14273773	1	1	yes	characteristic
414	C₂×C₄	#14273773	1	1	yes	characteristic
415	C₂×C₄	#14273773	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	236	2	no	—
420	C₈	C₄×D₂₃₆	1	1	yes	characteristic
421	C₈	C₄×D₂₃₆	1	1	yes	characteristic
422	C₈	C₄×D₂₃₆	1	1	yes	characteristic
423	C₈	C₄×D₂₃₆	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	944	2	no	—
426	C₂²	—	472	2	no	—
427	C₂²	—	472	4	no	—
428	C₂²	—	472	4	no	—
429	C₂²	—	236	2	no	—
430	C₂²	—	236	4	no	—
431	C₂²	#16837876	1	1	yes	characteristic
432	C₂²	#16837971	1	1	yes	characteristic
433	C₂²	#16838007	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	1	no	—
437	C₄	—	472	2	no	—
438	C₄	—	236	2	no	—
439	C₄	C₂×C₄×D₂₃₆	1	1	yes	characteristic
440	C₄	#16837876	1	1	yes	characteristic
441	C₄	#16837971	1	1	yes	characteristic
442	C₄	#16838007	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	472	4	no	—
447	C₂	—	472	2	no	—
448	C₂	#21426821	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21426821
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1747	C₂
socle	C₂×C₅₉	#2328
prime radical	#21434582	C₂
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1747	D₅₉
hypocenter	C₅₉	#22286
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1747

Complements

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

N	H ≅ G/N	type
2. #21433014	C₂	semidirect
3. #21432949	C₂	semidirect
4. #21425006	C₂	semidirect
5. #21424994	C₂	semidirect
6. #21424627	C₂	semidirect
7. #21424622	C₂	semidirect
8. #21424584	C₂	semidirect
9. #21424577	C₂	semidirect
10. #21424220	C₂	semidirect
11. C₅₉×#1747	C₂	semidirect
18. #16837791	C₄	semidirect
19. #16837786	C₄	semidirect
20. #16837779	C₄	semidirect
50. C₂×Dic₂₃₆	C₂×C₄	semidirect
51. C₂×#11745660	C₂×C₄	semidirect
52. C₂×#11745660	C₂×C₄	semidirect
59. C₂×D₄₇₂	C₂×C₄	semidirect
60. C₂×D₄₇₂	C₂×C₄	semidirect
65. #14273724	C₂×C₄	semidirect
66. #14273715	C₂×C₄	semidirect
91. #97×C₅₉	C₂×C₄	semidirect
92. #97×C₅₉	D₄	semidirect
94. C₄×C₈×C₅₉	C₂×C₄	semidirect
95. C₄×C₈×C₅₉	D₄	semidirect
229. #1747	D₅₉	semidirect
266. C₅₉	#22286	semidirect
316. #97	C₄×D₅₉	semidirect
317. #97	D₂₃₆	semidirect
319. C₄×C₈	C₄×D₅₉	semidirect
320. C₄×C₈	D₂₃₆	semidirect

Maximal subgroups

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

subgroup	index
#21434582	2
#21433014	2
#21432949	2
#21425006	2
#21424994	2
#21424627	2
#21424622	2
#21424584	2
#21424577	2
#21424220	2
C₅₉×#1747	2
#22286	59