Finite Group Databasebeta

← #28627204

Subgroups — #28627204

Order 15104.

1022 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837713C211yesmaximal, characteristic, complemented
2C2×#16837403C211yesmaximal, characteristic, complemented
3#21426971C211yesmaximal, characteristic, complemented
4#21425491C211yesmaximal, characteristic, complemented
5#21425484C211yesmaximal, characteristic, complemented
6#21425332C211yesmaximal, characteristic, complemented
7#21425327C211yesmaximal, characteristic, complemented
8#21425029C211yesmaximal, characteristic, complemented
9#21425024C211yesmaximal, characteristic, complemented
10#21424734C211yesmaximal, characteristic, complemented
11#21424713C211yesmaximal, characteristic, complemented
12#21424535C211yesmaximal, characteristic, complemented
13#21424281C211yesmaximal, characteristic, complemented
14#21424036C211yesmaximal, characteristic, complemented
15C59×#2431C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18#16837713—24no—
19C2×#14273660C2211yescharacteristic
20C2×#14273660C2211yescharacteristic
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×C4⋊(C59⋊C8)C2211yescharacteristic
23#16837403—24no—
24C2×#14273651C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×#14273648C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37#16837300C2211yescharacteristic
38#16837300C2211yescharacteristic
39#16837285—21no—
40#16837285—21no—
41#16837262C2211yescharacteristic
42#16837260—21no—
43C4×C4⋊Dic59C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic
45C22⋊C4×Dic59—21no—
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C22×#41×C59C2211yescharacteristic
51C2×#127×C59C2211yescharacteristic
52C2×#124×C59C2211yescharacteristic
53C2×#121×C59C2211yescharacteristic
54C59×#392—21no—
55C59×#392—21no—
56C59×#391C2211yescharacteristic
57C59×#390C2211yescharacteristic
58C59×#386—21no—
59C59×#386—21no—
60C4×C22⋊C4×C59C2211yescharacteristic
61C23×Dic59—21no—
62C2×#11745664—22no—
63C2×#11745664—41no—
64C2×#11745664—41no—
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59D414yescomplemented
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C2×C22⋊Dic59—21no—
79C2×C4×Dic59—21no—
80C2×C4×Dic59—21no—
81#14273660—22no—
82#14273660—22no—
83C4⋊(C59⋊C8)—41no—
84C4⋊(C59⋊C8)—41no—
85#14273651—22no—
86#14273651—22no—
87#14273651—22no—
88#14273651—41no—
89#14273648—22no—
90#14273648—22no—
91#14273648—22no—
92#14273648—22no—
93#14273648—22no—
94#14273648—41no—
95#14273648—41no—
96#14273648—41no—
97C22⋊(C59⋊C8)—22no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C2×#41×C59—22no—
104C2×#41×C59—22no—
105C2×#41×C59—22no—
106C2×#41×C59—22no—
107C2×#41×C59—41no—
108C2×#41×C59—41no—
109C22×Q8×C59C2311yescharacteristic
110C22×D4×C59—21no—
111C22×D4×C59—21no—
112C22×D4×C59—21no—
113C22×D4×C59—21no—
114C22×D4×C59C2311yescharacteristic
115C22×D4×C59C2311yescharacteristic
116C23×C4×C59—21no—
117C23×C4×C59C2311yescharacteristic
118#127×C59—22no—
119#127×C59—41no—
120#124×C59—22no—
121#124×C59—41no—
122#121×C59—22no—
123#121×C59—22no—
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C42×C59C2311yescharacteristic
133C2×C42×C59C2311yescharacteristic
134#95×C59—21no—
135#95×C59—21no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
138C24×C59—21no—
139C24×C59—21no—
140C24×C59C2×D411yescharacteristic
141#41×C59—28no—
142#41×C59—44no—
143#41×C59—44no—
144#41×C59—44no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59#4112yes—
151C2×D4×C59—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—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59—42no—
165C2×D4×C59—42no—
166C2×D4×C59—42no—
167C2×D4×C59—42no—
168C2×D4×C59—42no—
169C2×D4×C59—42no—
170C2×D4×C59—81no—
171C2×D4×C59—81no—
172C2×D4×C59—81no—
173C2×D4×C59—81no—
174C2×D4×C59#4112yes—
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—42no—
182C22×C4×C59—42no—
183C22×C4×C59—42no—
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D412yes—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59#4112yes—
191C22×C4×C59C2411yescharacteristic
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—24no—
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—81no—
198C22×Dic59—81no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C22⋊C4×C59—22no—
202C22⋊C4×C59—41no—
203C22⋊C4×C59—42no—
204C22⋊C4×C59—42no—
205C22⋊C4×C59—42no—
206C22⋊C4×C59—81no—
207C22⋊C4×C59—81no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—21no—
212C22⋊Dic59—42no—
213C4⋊Dic59—24no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59C2×D412yes—
221C4⋊Dic59C2×D412yes—
222Dic59⋊C4—81no—
223Dic59⋊C4—81no—
224C4×Dic59—81no—
225C4×Dic59—81no—
226#11745664—44no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—22no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59—41no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59#12112yes—
260C23×C59C22×D411yescharacteristic
261Q8×C59—22no—
262Q8×C59—22no—
263Q8×C59—41no—
264Q8×C59—41no—
265D4×C59—22no—
266D4×C59—22no—
267D4×C59—48no—
268D4×C59—41no—
269D4×C59—41no—
270D4×C59—41no—
271D4×C59—41no—
272D4×C59—41no—
273D4×C59—41no—
274D4×C59—84no—
275D4×C59—84no—
276D4×C59—84no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—22no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—21no—
295C2×C4×C59—48no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59#12112yes—
302C2×C4×C59#13712yes—
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4111yescharacteristic
305C2×C4×C59C2×#4111yescharacteristic
306C2×C4×C59C2×#4111yescharacteristic
307C2×C4×C59H(5,𝔽2)11yescharacteristic
308C2×C4×C59H(5,𝔽2)11yescharacteristic
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—84no—
322C59⋊C8—41no—
323C59⋊C8—41no—
324C59⋊C8—41no—
325C59⋊C8—41no—
326#24490—591nomaximal, Sylow
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—22no—
330C22×C59—41no—
331C22×C59—41no—
332C22×C59—41no—
333C22×C59—41no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—81no—
338C22×C59—81no—
339C22×C59—81no—
340C22×C59—81no—
341C22×C59—81no—
342C22×C59—81no—
343C22×C59—81no—
344C22×C59—81no—
345C22×C59—81no—
346C22×C59—81no—
347C22×C59—81no—
348C22×C59C2×#12111yescharacteristic
349C22×C59#54611yescharacteristic
350C22×C59#54611yescharacteristic
351C22×C59C2×#13711yescharacteristic
352C22×C59#57511yescharacteristic
353C22×C59#57611yescharacteristic
354C22×C59#57611yescharacteristic
355C4×C59—22no—
356C4×C59—22no—
357C4×C59—41no—
358C4×C59—42no—
359C4×C59—41no—
360C4×C59—41no—
361C4×C59—81no—
362C4×C59#52511yescharacteristic
363C4×C59#53511yescharacteristic
364C4×C59#55111yescharacteristic
365C4×C59#55111yescharacteristic
366Dic59—42no—
367Dic59—42no—
368Dic59—81no—
369Dic59—81no—
370C2×#480—591no—
371C2×#417—591no—
372#2431D5911yescharacteristic
373#2345—591no—
374#2068—591no—
375#2067—591no—
376#2042—591no—
377#2041—591no—
378#1983—591no—
379#1982—591no—
380#1928—591no—
381#1925—591no—
382#1895—591no—
383#1851—591no—
384#1788—591no—
385C2×C59—42no—
386C2×C59—82no—
387C2×C59—161no—
388C2×C59#241111yescharacteristic
389C2×C59#303711yescharacteristic
390C2×C59#304111yescharacteristic
391C2×C59#330911yescharacteristic
392C2×C59#331411yescharacteristic
393C2×C59#332211yescharacteristic
394C2×C59#333311yescharacteristic
395C22×#41C2×D5911yescharacteristic
396C22×M16—591no—
397C2×#127C2×D5911yescharacteristic
398C2×#124C2×D5911yescharacteristic
399C2×#121C2×D5911yescharacteristic
400C22×C4⋊C4—591no—
401#480—1184no—
402C2×#107—591no—
403C2×#107—591no—
404C2×C4⋊C8—591no—
405C2×C4⋊C8—591no—
406#417—1184no—
407C2×#103—591no—
408C2×#103—591no—
409C2×#103—591no—
410C2×#103—591no—
411C2×#102—591no—
412C2×#102—591no—
413C2×#102—591no—
414C2×#102—591no—
415C2×#102—591no—
416C2×#102—591no—
417C2×#102—591no—
418C2×#102—591no—
419C2×C22⋊C8—591no—
420#392—21no—
421#392—21no—
422#391C2×D5911yescharacteristic
423#390C2×D5911yescharacteristic
424#389—591no—
425#389—591no—
426#387—1181no—
427#387—1181no—
428#386—21no—
429#386—21no—
430#380—591no—
431#380—1181no—
432C4×C4⋊C4—591no—
433C4×C4⋊C4—591no—
434C4×C22⋊C4—1181no—
435C4×C22⋊C4C2×D5911yescharacteristic
436#340—591no—
437#340—591no—
438#336—591no—
439#336—591no—
440C59#2449011yescharacteristic, complemented, Sylow
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—41no—
446C2×#41—41no—
447C22×Q8C22×D5911yescharacteristic
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C22×D5911yescharacteristic
453C22×D4C22×D5911yescharacteristic
454C23×C4—21no—
455C23×C4—1181no—
456C23×C4C22×D5911yescharacteristic
457C2×M16—1182no—
458C2×M16—2361no—
459C2×M16—2361no—
460C22×C8—591no—
461C22×C8—591no—
462C22×C8—591no—
463C22×C8—591no—
464#127—22no—
465#127—41no—
466#124—22no—
467#124—41no—
468#121—22no—
469#121—22no—
470C2×C4⋊C4—594no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—591no—
475C2×C4⋊C4—1182no—
476C2×C4⋊C4—1181no—
477C2×C4⋊C4—1181no—
478C2×C4⋊C4—1181no—
479C2×C4⋊C4C22×D5911yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4C22⋊D5911yescharacteristic
487C2×C22⋊C4C22⋊D5911yescharacteristic
488C2×C42—1181no—
489C2×C42—1181no—
490C2×C42C22×D5911yescharacteristic
491C2×C42C22×D5911yescharacteristic
492#107—1182no—
493#107—1182no—
494C4⋊C8—2361no—
495C4⋊C8—2361no—
496#103—1182no—
497#103—1182no—
498#103—1182no—
499#103—2361no—
500#102—1182no—
501#102—1182no—
502#102—1182no—
503#102—1182no—
504#102—1182no—
505#102—2361no—
506#102—2361no—
507#102—2361no—
508C22⋊C8—1182no—
509#95—21no—
510#95—21no—
511#95—1181no—
512#95—1181no—
513#95—1181no—
514#95—1181no—
515#95—1181no—
516#95C22⋊D5911yescharacteristic
517#95C22⋊D5911yescharacteristic
518C24—21no—
519C24—21no—
520C24C2×C22⋊D5911yescharacteristic
521#41—28no—
522#41—44no—
523#41—44no—
524#41—44no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8#1174568712yes—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4#1174568712yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—1184no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—4721no—
570C22×C4—4721no—
571C22×C4D4×D5912yes—
572C22×C4#1174568712yes—
573C22×C4C2×C22⋊D5911yescharacteristic
574C22×C4C2×C22⋊D5911yescharacteristic
575C22×C4C2×C22⋊D5911yescharacteristic
576C22×C4C2×C22⋊D5911yescharacteristic
577C22×C4C2×C22⋊D5911yescharacteristic
578C22×C4C23×D5911yescharacteristic
579M16—2364no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C2×C8—1181no—
584C2×C8—1181no—
585C2×C8—1181no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—1181no—
591C2×C8—1181no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—592no—
595C4⋊C4—592no—
596C4⋊C4—1184no—
597C4⋊C4—1181no—
598C4⋊C4—1181no—
599C4⋊C4—1181no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—4721no—
604C4⋊C4—4721no—
605C22⋊C4—22no—
606C22⋊C4—41no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—2362no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—4721no—
618C42—4721no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23#1427369812yes—
640C23C22×C22⋊D5911yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—48no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655D4—84no—
656D4—84no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—4724no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4—2361no—
689C2×C4—2361no—
690C2×C4—2361no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4#1427369812yes—
695C2×C4#1427375712yes—
696C2×C4C2×D4×D5911yescharacteristic
697C2×C4C2×#1174568711yescharacteristic
698C2×C4C2×#1174568711yescharacteristic
699C2×C4C2×#1174568711yescharacteristic
700C2×C4#1427377211yescharacteristic
701C2×C4#1427377211yescharacteristic
702C8—2361no—
703C8—2361no—
704C8—2361no—
705C8—2361no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C2×#1427369811yescharacteristic
728C22#1683804611yescharacteristic
729C22#1683804611yescharacteristic
730C22C2×#1427375711yescharacteristic
731C22#1683820011yescharacteristic
732C22#1683820511yescharacteristic
733C22#1683820511yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—4721no—
742C4—4721no—
743C4—2362no—
744C4—2362no—
745C4#1683790811yescharacteristic
746C4#1683796711yescharacteristic
747C4#1683808311yescharacteristic
748C4#1683808311yescharacteristic
749C2—42no—
750C2—82no—
751C2—161no—
752C2#2142747711yescharacteristic
753C2#2143356411yescharacteristic
754C2#2143359511yescharacteristic
755C2#2143610211yescharacteristic
756C2#2143617711yescharacteristic
757C2#2143629711yescharacteristic
758C2#2143643411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC59×#2431C2
socleC23×C59C22×D4
hypercenter#2431D59
hypocenterC59#24490
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. C2×#16837713C2semidirect
2. C2×#16837403C2semidirect
3. #21426971C2semidirect
4. #21425491C2semidirect
5. #21425484C2semidirect
6. #21425332C2semidirect
7. #21425327C2semidirect
8. #21425029C2semidirect
9. #21425024C2semidirect
10. #21424734C2semidirect
11. #21424713C2semidirect
12. #21424535C2semidirect
13. #21424281C2semidirect
14. #21424036C2semidirect
71. C2×C4⋊Dic59D4semidirect
440. C59#24490semidirect

Maximal subgroups

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

subgroupindex
C2×#168377132
C2×#168374032
#214269712
#214254912
#214254842
#214253322
#214253272
#214250292
#214250242
#214247342
#214247132
#214245352
#214242812
#214240362
C59×#24312
#2449059