Finite Group Databasebeta

← #28735607

Subgroups — #28735607

Order 15104.

1140 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432378C211yesmaximal, characteristic, complemented
2#21425533C211yesmaximal, characteristic, complemented
3#21425532C211yesmaximal, characteristic, complemented
4#21425527C211yesmaximal, characteristic, complemented
5#21425285C211yesmaximal, characteristic, complemented
6#21425285C211yesmaximal, characteristic, complemented
7#21425282C211yesmaximal, characteristic, complemented
8#21425282C211yesmaximal, characteristic, complemented
9#21425278C211yesmaximal, characteristic, complemented
10#21425275C211yesmaximal, characteristic, complemented
11#21425092C211yesmaximal, characteristic, complemented
12#21425092C211yesmaximal, characteristic, complemented
13#21425092C211yesmaximal, characteristic, complemented
14#21424006C211yesmaximal, characteristic, complemented
15C59×#2847C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic, complemented
17C2×#14273701C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×#14273696—21no—
21C2×#14273660C2211yescharacteristic, complemented
22C2×#14273658C2211yescharacteristic, complemented
23C2×#14273658C2211yescharacteristic, complemented
24C2×#14273648C2211yescharacteristic, complemented
25C2×#14273648C2211yescharacteristic, complemented
26C2×#14273648C2211yescharacteristic, complemented
27C2×#14273647C2211yescharacteristic, complemented
28C2×#14273647C2211yescharacteristic, complemented
29C2×#14273647C2211yescharacteristic, complemented
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36#16837281—21no—
37#16837281—21no—
38#16837281—21no—
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837164C2211yescharacteristic, complemented
43#16837164C2211yescharacteristic, complemented
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48C24×C4×C59C2211yescharacteristic
49C2×#121×C59C2211yescharacteristic
50C2×#121×C59C2211yescharacteristic
51C2×#121×C59C2211yescharacteristic
52C2×#120×C59—21no—
53C59×#386—21no—
54C59×#386—21no—
55C59×#386—21no—
56C59×#380C2211yescharacteristic
57C59×#380C2211yescharacteristic
58C59×#380C2211yescharacteristic
59C22×D236C2311yescharacteristic
60C22×C22⋊D59—21no—
61C22×C22⋊D59—21no—
62C22×C22⋊D59—21no—
63C2×#11745669—41no—
64C2×#11745669—41no—
65C2×#11745669—41no—
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70#14273701—41no—
71#14273701—41no—
72#14273701—41no—
73#14273701—41no—
74#14273701—41no—
75#14273701—41no—
76#14273696—44no—
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86#14273660—41no—
87#14273658—41no—
88#14273658—41no—
89#14273648—41no—
90#14273648—41no—
91#14273648—41no—
92#14273647—41no—
93#14273647—41no—
94#14273647—41no—
95C22⋊(C59⋊C8)—41no—
96C22⋊(C59⋊C8)—41no—
97C22⋊(C59⋊C8)—41no—
98C22⋊(C59⋊C8)—41no—
99C22⋊(C59⋊C8)—41no—
100C22⋊(C59⋊C8)—41no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C25×C59D411yescharacteristic
105C22×D4×C59—21no—
106C22×D4×C59—21no—
107C22×D4×C59—21no—
108C22×D4×C59C2311yescharacteristic
109C23×C4×C59—41no—
110C23×C4×C59—41no—
111C23×C4×C59—41no—
112C23×C4×C59—41no—
113C23×C4×C59—41no—
114C23×C4×C59—41no—
115C23×C4×C59D411yescharacteristic
116C23×C4×C59D411yescharacteristic
117C23×C4×C59D411yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C23×C4×C59C2311yescharacteristic
120C23×C4×C59C2311yescharacteristic
121#121×C59—41no—
122#121×C59—41no—
123#121×C59—41no—
124#121×C59—41no—
125#121×C59—41no—
126#121×C59—41no—
127#120×C59—44no—
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—21no—
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140C24×C59—22no—
141C24×C59—22no—
142C24×C59—22no—
143C24×C59—21no—
144C24×C59—41no—
145C24×C59—41no—
146C24×C59—41no—
147C24×C59—41no—
148C24×C59C2×D411yescharacteristic
149C24×C59C2×D411yescharacteristic
150C24×C59C2×D411yescharacteristic
151C23×D59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—42no—
159C2×D4×C59—42no—
160C2×D4×C59—42no—
161C2×D4×C59—42no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59—42no—
165C2×D4×C59—42no—
166C2×D4×C59—42no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—41no—
189C22×C4×C59—41no—
190C22×C4×C59—41no—
191C22×C4×C59—41no—
192C22×C4×C59—41no—
193C22×C4×C59—41no—
194C22×C4×C59—41no—
195C22×C4×C59—41no—
196C22×C4×C59—41no—
197C22×C4×C59—44no—
198C22×C4×C59—44no—
199C22×C4×C59—44no—
200C22×C4×C59—44no—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2411yescharacteristic
205C2×C22⋊D59—42no—
206C2×C22⋊D59—42no—
207C2×C22⋊D59—42no—
208C2×C22⋊D59—42no—
209C2×C22⋊D59—42no—
210C2×C22⋊D59—42no—
211C2×C22⋊D59—42no—
212C2×C22⋊D59—42no—
213C2×C22⋊D59—42no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C2×D236—21no—
218C2×D236—21no—
219C2×D236—21no—
220C2×D236—21no—
221C2×D236—21no—
222C2×D236—21no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C22⋊C4×C59—42no—
230C22⋊C4×C59—42no—
231C22⋊C4×C59—42no—
232C22⋊C4×C59—42no—
233C22⋊C4×C59—42no—
234C22⋊C4×C59—42no—
235C22⋊Dic59—42no—
236C22⋊Dic59—42no—
237C22⋊Dic59—42no—
238#11745669—44no—
239(C2×D59)⋊C4—42no—
240(C2×D59)⋊C4—42no—
241(C2×D59)⋊C4—42no—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8—21no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—21no—
266C23×C59—21no—
267C23×C59—21no—
268C23×C59—21no—
269C23×C59—21no—
270C23×C59—21no—
271C23×C59—21no—
272C23×C59—21no—
273C23×C59—21no—
274C23×C59—21no—
275C23×C59—21no—
276C23×C59—21no—
277C23×C59—21no—
278C23×C59—44no—
279C23×C59—44no—
280C23×C59—44no—
281C23×C59—44no—
282C23×C59—44no—
283C23×C59—44no—
284C23×C59—44no—
285C23×C59—41no—
286C23×C59—41no—
287C23×C59—41no—
288C23×C59—41no—
289C23×C59—41no—
290C23×C59—41no—
291C23×C59—41no—
292C23×C59#13512yes—
293C23×C59AGL(1,ℤ/8)12yes—
294C23×C59AGL(1,ℤ/8)12yes—
295C23×C59C22×D411yescharacteristic
296C22×D59—41no—
297C22×D59—41no—
298C22×D59—41no—
299C22×D59—41no—
300C22×D59—41no—
301C22×D59—41no—
302C22×D59—41no—
303D4×C59—41no—
304D4×C59—41no—
305D4×C59—41no—
306D4×C59—41no—
307D4×C59—84no—
308D4×C59—84no—
309D4×C59—84no—
310C2×C4×C59—21no—
311C2×C4×C59—21no—
312C2×C4×C59—21no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—21no—
317C2×C4×C59—21no—
318C2×C4×C59—21no—
319C2×C4×C59—44no—
320C2×C4×C59—44no—
321C2×C4×C59—44no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—41no—
325C2×C4×C59—41no—
326C2×C4×C59—41no—
327C2×C4×C59—41no—
328C2×C4×C59—41no—
329C2×C4×C59—41no—
330C2×C4×C59—41no—
331C2×C4×C59—41no—
332C2×C4×C59—41no—
333C2×C4×C59—41no—
334C2×C4×C59—41no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59H(5,𝔽2)11yescharacteristic
344C2×C4×C59H(5,𝔽2)11yescharacteristic
345C2×C4×C59H(5,𝔽2)11yescharacteristic
346C2×C4×C59H(5,𝔽2)11yescharacteristic
347C2×C4×C59H(5,𝔽2)11yescharacteristic
348C2×C4×C59H(5,𝔽2)11yescharacteristic
349C22⋊D59—84no—
350C22⋊D59—84no—
351C22⋊D59—84no—
352C2×Dic59—41no—
353C2×Dic59—41no—
354C2×Dic59—41no—
355C2×Dic59—41no—
356C2×Dic59—41no—
357C2×Dic59—41no—
358C2×Dic59—41no—
359C2×Dic59—41no—
360C2×Dic59—41no—
361D236—41no—
362D236—41no—
363D236—41no—
364D236—41no—
365C59⋊C8—41no—
366C59⋊C8—41no—
367C59⋊C8—41no—
368C59⋊C8—41no—
369#32707—591nomaximal, Sylow
370C22×C59—22no—
371C22×C59—22no—
372C22×C59—22no—
373C22×C59—22no—
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—22no—
377C22×C59—22no—
378C22×C59—22no—
379C22×C59—416no—
380C22×C59—41no—
381C22×C59—41no—
382C22×C59—41no—
383C22×C59—41no—
384C22×C59—41no—
385C22×C59—41no—
386C22×C59—41no—
387C22×C59—41no—
388C22×C59—41no—
389C22×C59—41no—
390C22×C59—41no—
391C22×C59—41no—
392C22×C59—81no—
393C22×C59—81no—
394C22×C59—81no—
395C22×C59—81no—
396C22×C59—81no—
397C22×C59—81no—
398C22×C59—81no—
399C22×C59#53411yescharacteristic
400C22×C59#53411yescharacteristic
401C22×C59#53411yescharacteristic
402C22×C59C2×#13511yescharacteristic
403C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
404C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C59#57511yescharacteristic
406C2×D59—81no—
407C2×D59—81no—
408C2×D59—81no—
409C2×D59—81no—
410C2×D59—81no—
411C2×D59—81no—
412C2×D59—81no—
413C4×C59—41no—
414C4×C59—41no—
415C4×C59—41no—
416C4×C59—81no—
417C4×C59—81no—
418C4×C59—81no—
419C4×C59#56011yescharacteristic
420C4×C59#56011yescharacteristic
421C4×C59#56011yescharacteristic
422C4×C59H(3,𝔽4)11yescharacteristic
423Dic59—81no—
424Dic59—81no—
425Dic59—81no—
426#2847—591no—
427#2847D5911yescharacteristic, complemented
428#2077—591no—
429#2077—591no—
430#2076—591no—
431#2034—591no—
432#2034—591no—
433#2034—591no—
434#2034—591no—
435#2033—591no—
436#2033—591no—
437#1999—591no—
438#1999—591no—
439#1999—591no—
440#1779—591no—
441C2×C59—42no—
442C2×C59—42no—
443C2×C59—42no—
444C2×C59—161no—
445C2×C59#281211yescharacteristic
446C2×C59#318811yescharacteristic
447C2×C59#318811yescharacteristic
448C2×C59#319111yescharacteristic
449C2×C59#319211yescharacteristic
450C2×C59#319411yescharacteristic
451C2×C59#319411yescharacteristic
452D59—161no—
453C24×C4C2×D5911yescharacteristic
454C22×D8—591no—
455C2×#121—591no—
456C2×#121—591no—
457C2×#121—591no—
458C2×#121C2×D5911yescharacteristic
459C2×#121C2×D5911yescharacteristic
460C2×#121C2×D5911yescharacteristic
461C2×#120—21no—
462C2×#120—1181no—
463C2×#107—591no—
464C2×#106—591no—
465C2×#106—591no—
466C2×#102—591no—
467C2×#102—591no—
468C2×#102—591no—
469C2×#102—591no—
470C2×#102—591no—
471C2×#102—591no—
472C2×C22⋊C8—591no—
473C2×C22⋊C8—591no—
474C2×C22⋊C8—591no—
475C2×C22⋊C8—591no—
476C2×C22⋊C8—591no—
477C2×C22⋊C8—591no—
478#386—21no—
479#386—21no—
480#386—21no—
481#386—1181no—
482#386—1181no—
483#386—1181no—
484#380—591no—
485#380—591no—
486#380—591no—
487#380C2×D5911yescharacteristic
488#380C2×D5911yescharacteristic
489#380C2×D5911yescharacteristic
490#340—591no—
491#340—591no—
492#340—591no—
493#340—591no—
494#340—591no—
495#340—591no—
496C59#3270711yescharacteristic, complemented, Sylow
497C25C22⋊D5911yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—591no—
502C22×D4—1181no—
503C22×D4—1181no—
504C22×D4—1181no—
505C22×D4C22×D5911yescharacteristic
506C23×C4—41no—
507C23×C4—41no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4—41no—
511C23×C4—41no—
512C23×C4C22⋊D5911yescharacteristic
513C23×C4C22⋊D5911yescharacteristic
514C23×C4C22⋊D5911yescharacteristic
515C23×C4C22×D5911yescharacteristic
516C23×C4C22×D5911yescharacteristic
517C23×C4C22×D5911yescharacteristic
518C2×D8—2361no—
519C2×D8—2361no—
520C2×D8—2361no—
521C22×C8—591no—
522C22×C8—591no—
523C22×C8—591no—
524C22×C8—591no—
525#121—41no—
526#121—41no—
527#121—41no—
528#121—41no—
529#121—41no—
530#121—41no—
531#121—2361no—
532#121—2361no—
533#121—2361no—
534#121—2361no—
535#121—2361no—
536#121—2361no—
537#120—44no—
538#120—2364no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—591no—
541C2×C4⋊C4—591no—
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C4⋊C4C22×D5911yescharacteristic
544C2×C4⋊C4C22×D5911yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557#107—2361no—
558#106—2361no—
559#106—2361no—
560#102—2361no—
561#102—2361no—
562#102—2361no—
563#102—2361no—
564#102—2361no—
565#102—2361no—
566C22⋊C8—2361no—
567C22⋊C8—2361no—
568C22⋊C8—2361no—
569C22⋊C8—2361no—
570C22⋊C8—2361no—
571C22⋊C8—2361no—
572#95—21no—
573#95—21no—
574#95—21no—
575#95—1181no—
576#95—1181no—
577#95—1181no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—21no—
582C24—41no—
583C24—41no—
584C24—41no—
585C24—41no—
586C24—1181no—
587C24C2×C22⋊D5911yescharacteristic
588C24C2×C22⋊D5911yescharacteristic
589C24C2×C22⋊D5911yescharacteristic
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—1181no—
606C2×D4—1181no—
607C2×D4—1181no—
608C2×D4—1181no—
609C2×D4—1181no—
610C2×D4—1181no—
611C2×D4—2362no—
612C2×D4—2362no—
613C2×D4—2362no—
614C2×D4—2362no—
615C2×D4—2362no—
616C2×D4—2362no—
617C2×D4—2362no—
618C2×D4—2362no—
619C2×D4—2362no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—1181no—
655C22×C4—1181no—
656C22×C4—1181no—
657C22×C4C2×C22⋊D5911yescharacteristic
658C22×C4C2×C22⋊D5911yescharacteristic
659C22×C4C2×C22⋊D5911yescharacteristic
660C22×C4C23×D5911yescharacteristic
661D8—2364no—
662C2×C8—1181no—
663C2×C8—1181no—
664C2×C8—1181no—
665C2×C8—1181no—
666C2×C8—1181no—
667C2×C8—1181no—
668C2×C8—1181no—
669C2×C8—1181no—
670C2×C8—1181no—
671C2×C8—1181no—
672C2×C8—1181no—
673C2×C8—1181no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—1181no—
681C4⋊C4—1181no—
682C4⋊C4—1181no—
683C4⋊C4—1181no—
684C4⋊C4—1181no—
685C4⋊C4—1181no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—2362no—
693C22⋊C4—2362no—
694C22⋊C4—2362no—
695C22⋊C4—2362no—
696C22⋊C4—2362no—
697C22⋊C4—2362no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—2361no—
731C23—2361no—
732C23—2361no—
733C23—2361no—
734C23—2361no—
735C23—2361no—
736C23—2361no—
737C23#1427374712yes—
738C23#1427375212yes—
739C23#1427375312yes—
740C23C22×C22⋊D5911yescharacteristic
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—84no—
746D4—84no—
747D4—84no—
748D4—4724no—
749D4—4724no—
750D4—4724no—
751D4—2361no—
752D4—2361no—
753D4—2361no—
754D4—2361no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—2361no—
789C2×C4—2361no—
790C2×C4—2361no—
791C2×C4—2361no—
792C2×C4—2361no—
793C2×C4—2361no—
794C2×C4—2361no—
795C2×C4—2361no—
796C2×C4—2361no—
797C2×C4#1427377211yescharacteristic
798C2×C4#1427377211yescharacteristic
799C2×C4#1427377211yescharacteristic
800C2×C4#1427377211yescharacteristic
801C2×C4#1427377211yescharacteristic
802C2×C4#1427377211yescharacteristic
803C8—2361no—
804C8—2361no—
805C8—2361no—
806C8—2361no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—416no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—4721no—
837C22—4721no—
838C22—4721no—
839C22—4721no—
840C22—4721no—
841C22—4721no—
842C22—4721no—
843C22#1683796111yescharacteristic
844C22#1683796111yescharacteristic
845C22#1683796111yescharacteristic
846C22C2×#1427374711yescharacteristic
847C22C2×#1427375211yescharacteristic
848C22C2×#1427375311yescharacteristic
849C22#1683820011yescharacteristic
850C4—41no—
851C4—41no—
852C4—41no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4—4721no—
857C4—4721no—
858C4—4721no—
859C4#1683814111yescharacteristic
860C4#1683814111yescharacteristic
861C4#1683814111yescharacteristic
862C4#1683814511yescharacteristic
863C2—42no—
864C2—42no—
865C2—42no—
866C2—161no—
867C2—9441no—
868C2#2143209111yescharacteristic
869C2#2143485711yescharacteristic
870C2#2143486111yescharacteristic
871C2#2143488411yescharacteristic
872C2#2143489311yescharacteristic
873C2#2143490611yescharacteristic
874C2#2143491011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2847C2
socleC23×C59C22×D4
hypercenter#2847D59
hypocenterC59#32707
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. #21432378C2semidirect
2. #21425533C2semidirect
3. #21425532C2semidirect
4. #21425527C2semidirect
5. #21425285C2semidirect
6. #21425285C2semidirect
7. #21425282C2semidirect
8. #21425282C2semidirect
9. #21425278C2semidirect
10. #21425275C2semidirect
11. #21425092C2semidirect
12. #21425092C2semidirect
13. #21425092C2semidirect
14. #21424006C2semidirect
15. C59×#2847C2semidirect
16. C22×#11745669C22semidirect
21. C2×#14273660C22semidirect
22. C2×#14273658C22semidirect
23. C2×#14273658C22semidirect
24. C2×#14273648C22semidirect
25. C2×#14273648C22semidirect
26. C2×#14273648C22semidirect
27. C2×#14273647C22semidirect
28. C2×#14273647C22semidirect
29. C2×#14273647C22semidirect
42. #16837164C22semidirect
43. #16837164C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
427. #2847D59semidirect
496. C59#32707semidirect

Maximal subgroups

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

subgroupindex
#214323782
#214255332
#214255322
#214255272
#214252852
#214252822
#214252782
#214252752
#214250922
#214240062
C59×#28472
#3270759