Finite Group Databasebeta

← #28606012

Subgroups — #28606012

Order 15104.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837407C211yesmaximal, characteristic
2#21426983C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic59C211yesmaximal, characteristic
4#21424790C211yesmaximal, characteristic, complemented
5#21424776C211yesmaximal, characteristic, complemented
6#21424726C211yesmaximal, characteristic, complemented
7#21424719C211yesmaximal, characteristic, complemented
8#21424355C211yesmaximal, characteristic, complemented
9#21424341C211yesmaximal, characteristic, complemented
10#21424192C211yesmaximal, characteristic, complemented
11#21424127C211yesmaximal, characteristic, complemented
12#21423923C211yesmaximal, characteristic, complemented
13#102×Dic59C211yesmaximal, characteristic, complemented
14#21423882C211yesmaximal, characteristic, complemented
15C59×#1786C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C2×D4×Dic59C2211yescharacteristic
18C2×D4×Dic59C2211yescharacteristic
19C2×#14273686C2211yescharacteristic
20C22×C22⋊Dic59—21no—
21C2×#14273660C2211yescharacteristic, complemented
22C2×#14273658C2211yescharacteristic, complemented
23#16837407C418yescomplemented
24C2×#14273648C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273637C2211yescharacteristic, complemented
29C2×C8×Dic59C2211yescharacteristic, complemented
30#16837305C2211yescharacteristic
31#16837305C2211yescharacteristic
32#16837298C2211yescharacteristic, complemented
33#16837298C2211yescharacteristic, complemented
34#16837296—21no—
35#16837296—21no—
36#16837282—21no—
37#16837282—21no—
38#16837266—21no—
39#16837262C2211yescharacteristic
40#16837258—21no—
41C4⋊C4×Dic59C2211yescharacteristic, complemented
42C4⋊C4×Dic59C2211yescharacteristic, complemented
43C4×C22⋊Dic59C2211yescharacteristic
44#16837247—21no—
45#16837165C2211yescharacteristic, complemented
46#16837165C2211yescharacteristic, complemented
47#16837165C2211yescharacteristic, complemented
48#16837165C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837156C2211yescharacteristic, complemented
52#16837156C2211yescharacteristic, complemented
53C23×D4×C59C2211yescharacteristic
54C2×#102×C59C2211yescharacteristic
55C2×#102×C59C2211yescharacteristic
56C2×#102×C59C2211yescharacteristic
57C2×#102×C59C2211yescharacteristic
58C2×C22⋊C8×C59C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C23×Dic59—21no—
61C23×Dic59—21no—
62C2×#11745664—41no—
63C2×#11745664—41no—
64C2×#11745664C2×C414yescomplemented
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67D4×Dic59—22no—
68D4×Dic59—22no—
69D4×Dic59—41no—
70D4×Dic59—41no—
71#14273686—22no—
72#14273686C2×C414yescomplemented
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—44no—
88C2×C22⋊Dic59D411yescharacteristic
89C2×C22⋊Dic59D411yescharacteristic
90C2×C4×Dic59—21no—
91C2×C4×Dic59—21no—
92C2×C4×Dic59—21no—
93C2×C4×Dic59C2311yescharacteristic
94C2×C4×Dic59C2311yescharacteristic
95#14273660—41no—
96#14273658—41no—
97#14273648C2×C414yes—
98#14273648C2×C414yes—
99#14273648C2×C414yescomplemented
100#14273648C2×C414yescomplemented
101#14273637—41no—
102C8×Dic59—41no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95D411yescharacteristic
109C59⋊#95D411yescharacteristic
110C25×C59—21no—
111C22×D4×C59—22no—
112C22×D4×C59—22no—
113C22×D4×C59—21no—
114C22×D4×C59—22no—
115C22×D4×C59—41no—
116C22×D4×C59—41no—
117C22×D4×C59C2×C414yes—
118C22×D4×C59C2311yescharacteristic
119C22×D4×C59C2311yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C22×C8×C59C2311yescharacteristic
122C22×C8×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C22⋊C4×C59—21no—
126#102×C59—22no—
127#102×C59—22no—
128#102×C59—41no—
129#102×C59—41no—
130C22⋊C8×C59—22no—
131#95×C59—21no—
132C24×C59—21no—
133C24×C59—21no—
134C24×C59—24no—
135C24×C59—42no—
136C24×C59—42no—
137C24×C59—42no—
138C24×C59—42no—
139C24×C59—81no—
140C24×C59—81no—
141C24×C59C2×D411yescharacteristic
142C2×D4×C59—28no—
143C2×D4×C59—24no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—21no—
147C2×D4×C59—21no—
148C2×D4×C59—21no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—44no—
153C2×D4×C59—44no—
154C2×D4×C59—44no—
155C2×D4×C59—42no—
156C2×D4×C59—42no—
157C2×D4×C59C22×C412yes—
158C2×D4×C59C22×C412yes—
159C2×D4×C59#4112yes—
160C2×D4×C59#4112yes—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59C22×C412yes—
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59#4112yes—
170C22×C4×C59C2411yescharacteristic
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—42no—
176C22×Dic59—42no—
177C22×Dic59—42no—
178C22×Dic59—42no—
179C22×Dic59—81no—
180C22×Dic59—81no—
181C22×Dic59C2×D411yescharacteristic
182C22×Dic59C2×D411yescharacteristic
183C22×Dic59C2×D411yescharacteristic
184C22×Dic59C2×D411yescharacteristic
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C22⋊C4×C59—81no—
196C22⋊Dic59—24no—
197C22⋊Dic59—22no—
198C22⋊Dic59—41no—
199C22⋊Dic59—42no—
200C22⋊Dic59—42no—
201C22⋊Dic59—42no—
202C22⋊Dic59—42no—
203C22⋊Dic59—42no—
204C22⋊Dic59—81no—
205C22⋊Dic59—81no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59C22×C412yes—
213C4⋊Dic59C22×C412yes—
214Dic59⋊C4—81no—
215Dic59⋊C4—81no—
216C4×Dic59—24no—
217C4×Dic59—21no—
218C4×Dic59—21no—
219C4×Dic59—21no—
220C4×Dic59—21no—
221C4×Dic59—42no—
222C4×Dic59—42no—
223#11745664—44no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8C22×C412yes—
229C2×C59⋊C8C22×C412yes—
230C23×C59—22no—
231C23×C59—22no—
232C23×C59—22no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—22no—
240C23×C59—48no—
241C23×C59—48no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59—41no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—84no—
253C23×C59—84no—
254C23×C59—84no—
255C23×C59—84no—
256C23×C59—84no—
257C23×C59C4×D412yes—
258C23×C59C22×D411yescharacteristic
259D4×C59—22no—
260D4×C59—22no—
261D4×C59—22no—
262D4×C59—22no—
263D4×C59—22no—
264D4×C59—48no—
265D4×C59—41no—
266D4×C59—41no—
267D4×C59#11714yes—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59C4×D412yes—
281C2×C4×C59C23×C411yescharacteristic
282C2×C4×C59C2×#4111yescharacteristic
283C2×C4×C59C2×#4111yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59H(5,𝔽2)11yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×Dic59—21no—
288C2×Dic59—21no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—21no—
292C2×Dic59—21no—
293C2×Dic59—21no—
294C2×Dic59—21no—
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—84no—
311C2×Dic59—84no—
312C2×Dic59AGL(1,ℤ/8)12yes—
313C8×C59—41no—
314C8×C59—41no—
315C59⋊C8—22no—
316C59⋊C8—22no—
317#22584—591nomaximal, Sylow
318C22×C59—22no—
319C22×C59—24no—
320C22×C59—22no—
321C22×C59—22no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—42no—
325C22×C59—41no—
326C22×C59—41no—
327C22×C59—42no—
328C22×C59—41no—
329C22×C59—42no—
330C22×C59—42no—
331C22×C59—41no—
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—816no—
336C22×C59—81no—
337C22×C59—81no—
338C22×C59—81no—
339C22×C59—81no—
340C22×C59C2×C4×D411yescharacteristic
341C22×C59#54611yescharacteristic
342C22×C59#54611yescharacteristic
343C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C59#57511yescharacteristic
345C22×C59#57611yescharacteristic
346C22×C59#57711yescharacteristic
347C4×C59—22no—
348C4×C59—81no—
349C4×C59—81no—
350C4×C59C2×#11711yescharacteristic
351C4×C59#51811yescharacteristic
352C4×C59#55111yescharacteristic
353C4×C59#55111yescharacteristic
354Dic59—22no—
355Dic59—42no—
356Dic59—42no—
357Dic59—41no—
358Dic59—41no—
359Dic59—41no—
360Dic59—81no—
361Dic59—81no—
362C2×#418—591no—
363#2346—591no—
364D4×C22⋊C4—591no—
365#1936—591no—
366#1934—591no—
367#1926—591no—
368#1925—591no—
369#1864—591no—
370#1862—591no—
371#1825—591no—
372#1809—591no—
373#1786D5911yescharacteristic
374#1762—591no—
375C4×#102—591no—
376#1753—591no—
377C2×C59—42no—
378C2×C59—44no—
379C2×C59—82no—
380C2×C59#234211yescharacteristic
381C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C59#294611yescharacteristic
383C2×C59#331011yescharacteristic
384C2×C59#331911yescharacteristic
385C2×C59#332311yescharacteristic
386C2×C59#332511yescharacteristic
387C23×D4C2×D5911yescharacteristic
388C22×M16—591no—
389C2×C4×D4—591no—
390C2×C4×D4—591no—
391C2×#117—591no—
392C22×C22⋊C4—1181no—
393C2×#107—591no—
394C2×#106—591no—
395#418—598no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102—591no—
399C2×#102—591no—
400C2×#102C2×D5911yescharacteristic
401C2×#102C2×D5911yescharacteristic
402C2×#102C2×D5911yescharacteristic
403C2×#102C2×D5911yescharacteristic
404C2×C22⋊C8C2×D5911yescharacteristic
405C2×#97—591no—
406C2×C4×C8—591no—
407#390—591no—
408#390—591no—
409#389—591no—
410#389—591no—
411#388—1181no—
412#388—1181no—
413#386—1181no—
414#386—1181no—
415#382—1181no—
416#380—591no—
417#380C2×D5911yescharacteristic
418#379—1181no—
419C4×C4⋊C4—591no—
420C4×C4⋊C4—591no—
421C4×C22⋊C4—591no—
422#376—1181no—
423#340—591no—
424#340—591no—
425#340—591no—
426#340—591no—
427#340—591no—
428#340—591no—
429#336—591no—
430#336—591no—
431C59#2258411yescharacteristic, complemented, Sylow
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C4×D5914yes—
440C22×D4C22×D5911yescharacteristic
441C22×D4C22×D5911yescharacteristic
442C23×C4—1181no—
443C23×C4—1181no—
444C23×C4C22×D5911yescharacteristic
445C2×M16—594no—
446C2×M16—2361no—
447C2×M16—2361no—
448C22×C8—591no—
449C22×C8—591no—
450C22×C8C22×D5911yescharacteristic
451C22×C8C22×D5911yescharacteristic
452C4×D4—1182no—
453C4×D4—1182no—
454C4×D4—2361no—
455C4×D4—2361no—
456#117—594no—
457#117—1182no—
458C2×C4⋊C4—591no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—591no—
461C2×C4⋊C4—591no—
462C2×C4⋊C4—1181no—
463C2×C4⋊C4—1181no—
464C2×C4⋊C4C22×D5911yescharacteristic
465C2×C4⋊C4C22×D5911yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—591no—
468C2×C22⋊C4—591no—
469C2×C22⋊C4—1181no—
470C2×C22⋊C4—1181no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4—1181no—
473C2×C22⋊C4—1181no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4—1181no—
477C2×C22⋊C4—2364no—
478C2×C42—591no—
479C2×C42—591no—
480C2×C42—1181no—
481C2×C42—1181no—
482C2×C42—1181no—
483#107—2361no—
484#106—2361no—
485#102—22no—
486#102—22no—
487#102—41no—
488#102—41no—
489#102—594no—
490#102—594no—
491#102—594no—
492#102—594no—
493C22⋊C8—22no—
494#97—2361no—
495C4×C8—2361no—
496#95—21no—
497#95—591no—
498#95—591no—
499#95—1181no—
500#95—1181no—
501#95—1181no—
502#95—1181no—
503#95—1181no—
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24D4×D5911yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C2×C4×D5912yes—
530C2×D4C2×C4×D5912yes—
531C2×D4#1174568712yes—
532C2×D4#1174568712yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—591no—
540C22×C4—591no—
541C22×C4—591no—
542C22×C4—591no—
543C22×C4—1181no—
544C22×C4—1181no—
545C22×C4—1181no—
546C22×C4—1181no—
547C22×C4—4721no—
548C22×C4—4721no—
549C22×C4—2362no—
550C22×C4—2362no—
551C22×C4—2362no—
552C22×C4—2362no—
553C22×C4C2×C4×D5912yes—
554C22×C4D4×D5911yescharacteristic
555C22×C4#1174568712yes—
556C22×C4C23×D5911yescharacteristic
557M16—2364no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—592no—
565C2×C8—592no—
566C2×C8—1181no—
567C2×C8—1181no—
568C2×C8—1181no—
569C2×C8—1181no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—592no—
575C4⋊C4—592no—
576C4⋊C4—1181no—
577C4⋊C4—1181no—
578C4⋊C4—1181no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4—4721no—
583C4⋊C4—4721no—
584C22⋊C4—81no—
585C22⋊C4—1182no—
586C22⋊C4—1184no—
587C22⋊C4—4721no—
588C22⋊C4—4721no—
589C22⋊C4—2362no—
590C22⋊C4—2361no—
591C22⋊C4—2362no—
592C22⋊C4—2362no—
593C22⋊C4—2362no—
594C22⋊C4—2362no—
595C42—1184no—
596C42—1181no—
597C42—1181no—
598C42—1181no—
599C42—1181no—
600C42—2362no—
601C42—2362no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—22no—
608C23—21no—
609C23—21no—
610C23—22no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23(C22⋊D59)⋊C412yes—
630C23C2×D4×D5911yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1427368314yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—592no—
653C2×C4—1181no—
654C2×C4—1181no—
655C2×C4—1181no—
656C2×C4—1181no—
657C2×C4—1181no—
658C2×C4—1181no—
659C2×C4—1181no—
660C2×C4—1181no—
661C2×C4—1181no—
662C2×C4—1181no—
663C2×C4—1181no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—4724no—
667C2×C4—4724no—
668C2×C4—2361no—
669C2×C4—2361no—
670C2×C4—2361no—
671C2×C4—2361no—
672C2×C4—2361no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4(C22⋊D59)⋊C412yes—
679C2×C4C22×C4×D5911yescharacteristic
680C2×C4C2×#1174568711yescharacteristic
681C2×C4C2×#1174568711yescharacteristic
682C2×C4C2×#1174568711yescharacteristic
683C2×C4#1427377211yescharacteristic
684C2×C4#1427377211yescharacteristic
685C8—41no—
686C8—41no—
687C8—1182no—
688C8—1182no—
689C22—22no—
690C22—24no—
691C22—22no—
692C22—22no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×(C22⋊D59)⋊C411yescharacteristic
712C22#1683803911yescharacteristic
713C22#1683803911yescharacteristic
714C22AGL(1,ℤ/8)×D5911yescharacteristic
715C22#1683819811yescharacteristic
716C22#1683820311yescharacteristic
717C22#1683820811yescharacteristic
718C4—22no—
719C4—81no—
720C4—81no—
721C4—1182no—
722C4—4721no—
723C4—4721no—
724C4—2362no—
725C4—2361no—
726C4—2362no—
727C4—2361no—
728C4—2361no—
729C4C2×#1427368311yescharacteristic
730C4#1683787511yescharacteristic
731C4#1683808311yescharacteristic
732C4#1683808311yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#2142694711yescharacteristic
737C2#2143290011yescharacteristic
738C2#2143292211yescharacteristic
739C2#2143611011yescharacteristic
740C2#2143624511yescharacteristic
741C2#2143631611yescharacteristic
742C2#2143633111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1786C2
socleC23×C59C22×D4
prime radicalC23×D4×C59C22
cosocleC22×C4×C59C24
hypercenter#1786D59
hypocenterC59#22584
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #21426983C2semidirect
4. #21424790C2semidirect
5. #21424776C2semidirect
6. #21424726C2semidirect
7. #21424719C2semidirect
8. #21424355C2semidirect
9. #21424341C2semidirect
10. #21424192C2semidirect
11. #21424127C2semidirect
12. #21423923C2semidirect
13. #102×Dic59C2semidirect
14. #21423882C2semidirect
21. C2×#14273660C22semidirect
22. C2×#14273658C22semidirect
23. #16837407C4semidirect
28. C2×#14273637C22semidirect
29. C2×C8×Dic59C22semidirect
32. #16837298C22semidirect
33. #16837298C22semidirect
41. C4⋊C4×Dic59C22semidirect
42. C4⋊C4×Dic59C22semidirect
45. #16837165C22semidirect
46. #16837165C22semidirect
47. #16837165C22semidirect
48. #16837165C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
51. #16837156C22semidirect
52. #16837156C22semidirect
64. C2×#11745664C2×C4semidirect
72. #14273686C2×C4semidirect
99. #14273648C2×C4semidirect
100. #14273648C2×C4semidirect
431. C59#22584semidirect

Maximal subgroups

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

subgroupindex
C2×#168374072
#214269832
D4×C22⋊Dic592
#214247902
#214247762
#214247262
#214247192
#214243552
#214243412
#214241922
#214241272
#214239232
#102×Dic592
#214238822
C59×#17862
#2258459