Finite Group Databasebeta

← #28645153

Subgroups — #28645153

Order 15104.

1292 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837756C211yesmaximal, characteristic, complemented
2C2×#16837709C211yesmaximal, characteristic, complemented
3#21429262C211yesmaximal, characteristic, complemented
4#21425296C211yesmaximal, characteristic, complemented
5#21425289C211yesmaximal, characteristic, complemented
6#21425282C211yesmaximal, characteristic, complemented
7#21425275C211yesmaximal, characteristic, complemented
8#21425029C211yesmaximal, characteristic, complemented
9#21424891C211yesmaximal, characteristic, complemented
10#21424036C211yesmaximal, characteristic, complemented
11#21424036C211yesmaximal, characteristic, complemented
12#21424031C211yesmaximal, characteristic, complemented
13#21424031C211yesmaximal, characteristic, complemented
14C4×#14273651C211yesmaximal, characteristic, complemented
15C2×C59×#548C211yesmaximal, characteristic
16C2×#14273719C2211yescharacteristic
17#16837756—24no—
18#16837709—24no—
19C2×#14273660C2211yescharacteristic
20C2×#14273658C2211yescharacteristic
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×#14273651C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38C2×C4×C59⋊C8C2211yescharacteristic
39#16837340—21no—
40#16837316—21no—
41#16837296—21no—
42#16837296—21no—
43#16837262C2211yescharacteristic
44#16837262C2211yescharacteristic
45#16837262C2211yescharacteristic
46#16837262C2211yescharacteristic
47C4×C4⋊Dic59C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C22×#41×C59C2211yescharacteristic
51C23×Q8×C59C2211yescharacteristic
52C59×#548—24no—
53C59×#548—24no—
54C2×#124×C59—21no—
55C2×#124×C59C2211yescharacteristic
56C2×C22⋊Q8×C59—21no—
57C2×C22⋊Q8×C59C2211yescharacteristic
58C2×#121×C59—21no—
59C2×#121×C59C2211yescharacteristic
60C2×C4×Q8×C59C2211yescharacteristic
61C2×C4×D4×C59—21no—
62C2×C4×D4×C59C2211yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67#14273719—22no—
68#14273719—22no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×C22⋊Dic59—21no—
76C2×C22⋊Dic59—21no—
77C2×C22⋊Dic59—21no—
78C2×C22⋊Dic59—21no—
79C2×C4×Dic59—21no—
80#14273660—22no—
81#14273658—22no—
82C4⋊(C59⋊C8)—22no—
83#14273651—22no—
84#14273651—22no—
85#14273651—22no—
86#14273651—22no—
87#14273651—22no—
88#14273651—22no—
89#14273651—41no—
90#14273651—41no—
91#14273648—22no—
92#14273648—22no—
93#14273648—41no—
94#14273648—41no—
95C22⋊(C59⋊C8)—41no—
96C22⋊(C59⋊C8)—41no—
97C22⋊(C59⋊C8)—41no—
98C22⋊(C59⋊C8)—41no—
99C4×C59⋊C8—22no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C2×#41×C59—22no—
106C2×#41×C59—22no—
107C2×#41×C59—22no—
108C2×#41×C59—22no—
109C2×#41×C59—41no—
110C2×#41×C59—41no—
111C22×Q8×C59—22no—
112C22×Q8×C59—22no—
113C22×Q8×C59—21no—
114C22×Q8×C59—22no—
115C22×Q8×C59—22no—
116C22×Q8×C59—41no—
117C22×Q8×C59—41no—
118C22×Q8×C59C2311yescharacteristic
119C22×Q8×C59C2311yescharacteristic
120C22×D4×C59—21no—
121C22×D4×C59—21no—
122C22×D4×C59D411yescharacteristic
123C22×D4×C59C2311yescharacteristic
124C23×C4×C59—21no—
125C23×C4×C59—21no—
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128#124×C59—28no—
129#124×C59—22no—
130#124×C59D414yes—
131C22⋊Q8×C59—28no—
132C22⋊Q8×C59—22no—
133C22⋊Q8×C59—22no—
134#121×C59—28no—
135#121×C59—22no—
136#121×C59—22no—
137C4×Q8×C59—22no—
138C4×Q8×C59D414yes—
139C4×D4×C59—28no—
140C4×D4×C59—22no—
141C4×D4×C59—22no—
142C2×C4⋊C4×C59—21no—
143C2×C4⋊C4×C59—21no—
144C2×C4⋊C4×C59D411yescharacteristic
145C2×C4⋊C4×C59C2311yescharacteristic
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59—21no—
148C2×C22⋊C4×C59—21no—
149C2×C22⋊C4×C59—21no—
150C2×C22⋊C4×C59D411yescharacteristic
151C2×C22⋊C4×C59D411yescharacteristic
152C2×C42×C59—21no—
153C2×C42×C59C2311yescharacteristic
154C24×C59—21no—
155C24×C59C2×D411yescharacteristic
156C24×C59C2×D411yescharacteristic
157#41×C59—44no—
158#41×C59—44no—
159#41×C59—44no—
160#41×C59—44no—
161C2×Q8×C59—24no—
162C2×Q8×C59—21no—
163C2×Q8×C59—21no—
164C2×Q8×C59—21no—
165C2×Q8×C59—21no—
166C2×Q8×C59—21no—
167C2×Q8×C59—21no—
168C2×Q8×C59—21no—
169C2×Q8×C59—21no—
170C2×Q8×C59—42no—
171C2×Q8×C59—42no—
172C2×Q8×C59—44no—
173C2×Q8×C59—44no—
174C2×Q8×C59—44no—
175C2×Q8×C59—44no—
176C2×Q8×C59C2×D412yes—
177C2×Q8×C59C2×D412yes—
178C2×Q8×C59#4112yes—
179C2×Q8×C59#4112yes—
180C2×D4×C59—24no—
181C2×D4×C59—24no—
182C2×D4×C59—22no—
183C2×D4×C59—22no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—41no—
190C2×D4×C59—42no—
191C2×D4×C59—42no—
192C2×D4×C59—42no—
193C2×D4×C59—42no—
194C2×D4×C59C2×D412yes—
195C22×C4×C59—21no—
196C22×C4×C59—24no—
197C22×C4×C59—24no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—42no—
213C22×C4×C59—42no—
214C22×C4×C59—42no—
215C22×C4×C59—42no—
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2411yescharacteristic
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—22no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59C2×D412yes—
230C22⋊C4×C59—24no—
231C22⋊C4×C59—24no—
232C22⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59—22no—
236C42×C59—24no—
237C42×C59C2×D412yes—
238C42×C59C2×D412yes—
239C22⋊Dic59—42no—
240C22⋊Dic59—42no—
241C22⋊Dic59—81no—
242C22⋊Dic59—81no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251Dic59⋊C4—42no—
252Dic59⋊C4—42no—
253C4×Dic59—81no—
254C2×C59⋊C8—21no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—21no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8—21no—
262C2×C59⋊C8—21no—
263C2×C59⋊C8—21no—
264C2×C59⋊C8—21no—
265C2×C59⋊C8—21no—
266C23×C59—21no—
267C23×C59—21no—
268C23×C59—21no—
269C23×C59—21no—
270C23×C59—21no—
271C23×C59—21no—
272C23×C59—21no—
273C23×C59—22no—
274C23×C59—21no—
275C23×C59—21no—
276C23×C59—21no—
277C23×C59—21no—
278C23×C59—21no—
279C23×C59—21no—
280C23×C59—41no—
281C23×C59—41no—
282C23×C59—41no—
283C23×C59—41no—
284C23×C59—41no—
285C23×C59—41no—
286C23×C59#13512yes—
287C23×C59C22×D411yescharacteristic
288Q8×C59—22no—
289Q8×C59—22no—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—22no—
293Q8×C59—48no—
294Q8×C59—41no—
295Q8×C59—41no—
296Q8×C59#12414yes—
297D4×C59—22no—
298D4×C59—22no—
299D4×C59—44no—
300D4×C59—48no—
301D4×C59—48no—
302D4×C59—41no—
303D4×C59—41no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—21no—
308C2×C4×C59—21no—
309C2×C4×C59—21no—
310C2×C4×C59—21no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
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—48no—
320C2×C4×C59—48no—
321C2×C4×C59—41no—
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#12012yes—
334C2×C4×C59#12012yes—
335C2×C4×C59C22×D411yescharacteristic
336C2×C4×C59C22×D411yescharacteristic
337C2×C4×C59C2×#4111yescharacteristic
338C2×C4×C59C2×#4111yescharacteristic
339C2×C4×C59H(5,𝔽2)11yescharacteristic
340C2×C4×C59H(5,𝔽2)11yescharacteristic
341C2×Dic59—41no—
342C2×Dic59—41no—
343C2×Dic59—41no—
344C2×Dic59—41no—
345C2×Dic59—41no—
346C2×Dic59—41no—
347C2×Dic59—41no—
348C2×Dic59—41no—
349C2×Dic59—41no—
350C2×Dic59—41no—
351C2×Dic59—41no—
352C2×Dic59—41no—
353C59⋊C8—41no—
354C59⋊C8—41no—
355C59⋊C8—41no—
356C59⋊C8—41no—
357#25889—591nomaximal, Sylow
358C22×C59—22no—
359C22×C59—22no—
360C22×C59—22no—
361C22×C59—41no—
362C22×C59—41no—
363C22×C59—41no—
364C22×C59—41no—
365C22×C59—42no—
366C22×C59—41no—
367C22×C59—41no—
368C22×C59—42no—
369C22×C59—41no—
370C22×C59—42no—
371C22×C59—41no—
372C22×C59—41no—
373C22×C59—41no—
374C22×C59—41no—
375C22×C59—81no—
376C22×C59—81no—
377C22×C59—81no—
378C22×C59—81no—
379C22×C59C2×#12011yescharacteristic
380C22×C59#54611yescharacteristic
381C22×C59#54611yescharacteristic
382C22×C59C2×#13511yescharacteristic
383C22×C59#57511yescharacteristic
384C22×C59#57711yescharacteristic
385C22×C59#57811yescharacteristic
386C4×C59—24no—
387C4×C59—22no—
388C4×C59—22no—
389C4×C59—41no—
390C4×C59—41no—
391C4×C59—42no—
392C4×C59—42no—
393C4×C59C2×#12411yescharacteristic
394C4×C59#53511yescharacteristic
395C4×C59#54611yescharacteristic
396C4×C59#54611yescharacteristic
397Dic59—81no—
398Dic59—81no—
399Dic59—81no—
400Dic59—81no—
401C2×#548D5911yescharacteristic
402C2×#488—591no—
403C2×#479—591no—
404#2562—591no—
405#2036—591no—
406#2035—591no—
407#2034—591no—
408#2033—591no—
409#1983—591no—
410#1954—591no—
411#1788—591no—
412#1788—591no—
413#1787—591no—
414#1787—591no—
415C4×#103—591no—
416C2×C59—42no—
417C2×C59—81no—
418C2×C59—82no—
419C2×C59#243511yescharacteristic
420C2×C59#300211yescharacteristic
421C2×C59#301311yescharacteristic
422C2×C59#330011yescharacteristic
423C2×C59#330111yescharacteristic
424C2×C59#332611yescharacteristic
425C2×C59#332711yescharacteristic
426C22×#41C2×D5911yescharacteristic
427C23×Q8C2×D5911yescharacteristic
428#548—24no—
429#548—24no—
430C2×#125—591no—
431C2×#124—21no—
432C2×#124C2×D5911yescharacteristic
433C2×C22⋊Q8—21no—
434C2×C22⋊Q8C2×D5911yescharacteristic
435C2×#121—21no—
436C2×#121C2×D5911yescharacteristic
437C2×C4×Q8C2×D5911yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4C2×D5911yescharacteristic
440#488—1184no—
441#479—1184no—
442C2×#107—591no—
443C2×#106—591no—
444C2×C4⋊C8—591no—
445C2×#103—591no—
446C2×#103—591no—
447C2×#103—591no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#102—591no—
454C2×#102—591no—
455C2×#102—591no—
456C2×#102—591no—
457C2×C22⋊C8—591no—
458C2×C22⋊C8—591no—
459C2×C22⋊C8—591no—
460C2×C22⋊C8—591no—
461C2×C4×C8—591no—
462#400—1181no—
463#394—1181no—
464#388—1181no—
465#388—1181no—
466#380—591no—
467#380—591no—
468#380—591no—
469#380—591no—
470C4×C4⋊C4—591no—
471#340—591no—
472#340—591no—
473C59#2588911yescharacteristic, complemented, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8—22no—
481C22×Q8—22no—
482C22×Q8—21no—
483C22×Q8—22no—
484C22×Q8—22no—
485C22×Q8—41no—
486C22×Q8—41no—
487C22×Q8C22×D5911yescharacteristic
488C22×Q8C22×D5911yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C22⋊D5911yescharacteristic
492C22×D4C22×D5911yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4C22×D5911yescharacteristic
496C23×C4C22×D5911yescharacteristic
497C22×C8—591no—
498C22×C8—591no—
499C22×C8—591no—
500C22×C8—591no—
501#125—1182no—
502#125—1182no—
503#124—28no—
504#124—22no—
505#124C22⋊D5914yes—
506C22⋊Q8—28no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509#121—28no—
510#121—22no—
511#121—22no—
512C4×Q8—22no—
513C4×Q8C22⋊D5914yes—
514C4×D4—28no—
515C4×D4—22no—
516C4×D4—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4C22⋊D5911yescharacteristic
526C2×C4⋊C4C22×D5911yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4C22⋊D5911yescharacteristic
536C2×C22⋊C4C22⋊D5911yescharacteristic
537C2×C42—21no—
538C2×C42—1181no—
539C2×C42C22×D5911yescharacteristic
540#107—1182no—
541#106—1182no—
542C4⋊C8—1182no—
543#103—1182no—
544#103—1182no—
545#103—1182no—
546#103—1182no—
547#103—1182no—
548#103—1182no—
549#103—2361no—
550#103—2361no—
551#102—1182no—
552#102—1182no—
553#102—2361no—
554#102—2361no—
555C22⋊C8—2361no—
556C22⋊C8—2361no—
557C22⋊C8—2361no—
558C22⋊C8—2361no—
559C4×C8—1182no—
560#95—1181no—
561#95—1181no—
562#95—1181no—
563#95—1181no—
564#95—1181no—
565C24—21no—
566C24C2×C22⋊D5911yescharacteristic
567C24C2×C22⋊D5911yescharacteristic
568#41—44no—
569#41—44no—
570#41—44no—
571#41—44no—
572C2×Q8—24no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—42no—
582C2×Q8—42no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8#1174568712yes—
588C2×Q8#1174568712yes—
589C2×Q8C2×C22⋊D5912yes—
590C2×Q8C2×C22⋊D5912yes—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4C2×C22⋊D5912yes—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—1181no—
628C22×C4—1181no—
629C22×C4—1181no—
630C22×C4—1181no—
631C22×C4C2×C22⋊D5911yescharacteristic
632C22×C4C2×C22⋊D5911yescharacteristic
633C22×C4C2×C22⋊D5911yescharacteristic
634C22×C4C2×C22⋊D5911yescharacteristic
635C22×C4C23×D5911yescharacteristic
636C2×C8—1181no—
637C2×C8—1181no—
638C2×C8—1181no—
639C2×C8—1181no—
640C2×C8—1181no—
641C2×C8—1181no—
642C2×C8—1181no—
643C2×C8—1181no—
644C2×C8—1181no—
645C2×C8—1181no—
646C2×C8—1181no—
647C2×C8—1181no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—1181no—
653C4⋊C4—1181no—
654C4⋊C4—1181no—
655C4⋊C4—1181no—
656C4⋊C4—1181no—
657C4⋊C4—1181no—
658C4⋊C4—1181no—
659C4⋊C4—1181no—
660C4⋊C4—2362no—
661C4⋊C4—2362no—
662C4⋊C4C2×C22⋊D5912yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—4721no—
670C22⋊C4—4721no—
671C22⋊C4—2362no—
672C22⋊C4—2362no—
673C42—24no—
674C42—4721no—
675C42C2×C22⋊D5912yes—
676C42C2×C22⋊D5912yes—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23#1427374712yes—
698C23C22×C22⋊D5911yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—48no—
705Q8—41no—
706Q8—41no—
707Q8#1427371414yes—
708D4—22no—
709D4—22no—
710D4—44no—
711D4—48no—
712D4—48no—
713D4—41no—
714D4—41no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—2361no—
745C2×C4—2361no—
746C2×C4—2361no—
747C2×C4—2361no—
748C2×C4—2361no—
749C2×C4—2361no—
750C2×C4—2361no—
751C2×C4—2361no—
752C2×C4—2361no—
753C2×C4—2361no—
754C2×C4—2361no—
755C2×C4—2361no—
756C2×C4#1427369612yes—
757C2×C4#1427369612yes—
758C2×C4C22×C22⋊D5911yescharacteristic
759C2×C4C22×C22⋊D5911yescharacteristic
760C2×C4C2×#1174568711yescharacteristic
761C2×C4C2×#1174568711yescharacteristic
762C2×C4#1427377211yescharacteristic
763C2×C4#1427377211yescharacteristic
764C8—2361no—
765C8—2361no—
766C8—2361no—
767C8—2361no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#1427369611yescharacteristic
790C22#1683804611yescharacteristic
791C22#1683804611yescharacteristic
792C22C2×#1427374711yescharacteristic
793C22#1683820011yescharacteristic
794C22#1683821011yescharacteristic
795C22#1683821711yescharacteristic
796C4—24no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—41no—
801C4—42no—
802C4—42no—
803C4—4721no—
804C4—4721no—
805C4—4721no—
806C4—4721no—
807C4C2×#1427371411yescharacteristic
808C4#1683796911yescharacteristic
809C4#1683804611yescharacteristic
810C4#1683804611yescharacteristic
811C2—42no—
812C2—81no—
813C2—82no—
814C2#2142774311yescharacteristic
815C2#2143331411yescharacteristic
816C2#2143341111yescharacteristic
817C2#2143598311yescharacteristic
818C2#2143599811yescharacteristic
819C2#2143634911yescharacteristic
820C2#2143636411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#548C2
socleC23×C59C22×D4
hypercenterC2×#548D59
hypocenterC59#25889
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16837756C2semidirect
2. C2×#16837709C2semidirect
3. #21429262C2semidirect
4. #21425296C2semidirect
5. #21425289C2semidirect
6. #21425282C2semidirect
7. #21425275C2semidirect
8. #21425029C2semidirect
9. #21424891C2semidirect
10. #21424036C2semidirect
11. #21424036C2semidirect
12. #21424031C2semidirect
13. #21424031C2semidirect
14. C4×#14273651C2semidirect
473. C59#25889semidirect

Maximal subgroups

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

subgroupindex
C2×#168377562
C2×#168377092
#214292622
#214252962
#214252892
#214252822
#214252752
#214250292
#214248912
#214240362
#214240312
C4×#142736512
C2×C59×#5482
#2588959