Finite Group Databasebeta

← #28595167

Subgroups — #28595167

Order 15104.

1138 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837633C211yesmaximal, characteristic
2C2×#16837487C211yesmaximal, characteristic, complemented
3C22×C8×Dic59C211yesmaximal, characteristic, complemented
4C22⋊Q8×Dic59C211yesmaximal, characteristic, complemented
5#21426602C211yesmaximal, characteristic
6#21424947C211yesmaximal, characteristic, complemented
7#21424823C211yesmaximal, characteristic, complemented
8#21424780C211yesmaximal, characteristic, complemented
9#21424769C211yesmaximal, characteristic, complemented
10#21424524C211yesmaximal, characteristic
11#21424119C211yesmaximal, characteristic, complemented
12#21423984C211yesmaximal, characteristic, complemented
13#103×Dic59C211yesmaximal, characteristic, complemented
14#21423910C211yesmaximal, characteristic, complemented
15C59×#1892C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×Q8×Dic59C2211yescharacteristic
20C2×#14273689C2211yescharacteristic
21C2×(C22⋊D59)⋊C4—21no—
22C22×C4×Dic59C2211yescharacteristic
23#16837633C418yescomplemented
24#16837487—24no—
25C2×#14273658C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27C2×#14273658C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273649C2211yescharacteristic
30C2×#14273649C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×C8×Dic59—24no—
33C2×C8×Dic59C2211yescharacteristic
34C2×C8×Dic59C2211yescharacteristic
35C2×C8×Dic59C2211yescharacteristic
36C2×C8×Dic59C2211yescharacteristic
37#16837309C2211yescharacteristic
38#16837303C2211yescharacteristic
39#16837301C2211yescharacteristic
40#16837298C2211yescharacteristic
41#16837291—21no—
42#16837288—21no—
43#16837279—21no—
44#16837277—21no—
45#16837262C2211yescharacteristic
46C4⋊C4×Dic59—21no—
47C4⋊C4×Dic59C2211yescharacteristic
48C4⋊C4×Dic59C2211yescharacteristic
49C22⋊C4×Dic59—21no—
50#16837249—21no—
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53#16837164C2211yescharacteristic
54#16837164C2211yescharacteristic
55C23×C8×C59C2211yescharacteristic
56C2×C22⋊Q8×C59C2211yescharacteristic
57C2×#103×C59C2211yescharacteristic
58C2×#103×C59C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C23×Dic59D411yescharacteristic
65C23×Dic59D411yescharacteristic
66C22×C4×D59—21no—
67C2×#11745671—22no—
68C2×#11745671—22no—
69C2×#11745671C2×C414yescomplemented
70C22×C59⋊C8—22no—
71C22×C59⋊C8—22no—
72C22×C59⋊C8C2×C414yescomplemented
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273701—22no—
76#14273701C2×C414yes—
77Q8×Dic59—22no—
78Q8×Dic59—22no—
79#14273689—22no—
80#14273689—22no—
81(C22⋊D59)⋊C4—44no—
82C2×C4⋊Dic59—21no—
83C2×C4⋊Dic59—21no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×Dic59⋊C4—21no—
88C2×C22⋊Dic59—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×C4×Dic59—22no—
94C2×C4×Dic59—22no—
95C2×C4×Dic59—21no—
96C2×C4×Dic59—21no—
97C2×C4×Dic59—21no—
98C2×C4×Dic59D411yescharacteristic
99C2×C4×Dic59D411yescharacteristic
100C2×C4×Dic59C2311yescharacteristic
101C2×C4×Dic59C2311yescharacteristic
102#14273658—22no—
103#14273658—22no—
104#14273658C2×C414yescomplemented
105#14273651C2×C414yescomplemented
106#14273649—22no—
107#14273649—22no—
108#14273647C2×C414yescomplemented
109C8×Dic59—22no—
110C8×Dic59—22no—
111C8×Dic59—22no—
112C8×Dic59D414yescomplemented
113C59⋊#95—21no—
114C59⋊#95—21no—
115C59⋊#95—21no—
116C59⋊#95—21no—
117C59⋊#95—21no—
118C59⋊#95—21no—
119C59⋊#95—21no—
120C22×Q8×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C22×C8×C59—22no—
123C22×C8×C59—22no—
124C22×C8×C59—22no—
125C22×C8×C59C2311yescharacteristic
126C22×C8×C59C2311yescharacteristic
127C22⋊Q8×C59—22no—
128C22⋊Q8×C59C2×C414yescomplemented
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C4⋊C4×C59C2311yescharacteristic
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135#103×C59—22no—
136#103×C59—22no—
137#95×C59—21no—
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59C22×C412yes—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59C22×C412yes—
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59#4112yes—
157C22×C4×C59C2411yescharacteristic
158C2×C22⋊D59—24no—
159C2×C22⋊D59—42no—
160C2×C22⋊D59—42no—
161C22×Dic59—22no—
162C22×Dic59—22no—
163C22×Dic59—22no—
164C22×Dic59—22no—
165C22×Dic59—22no—
166C22×Dic59—21no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59SD1614yescomplemented
170C22×Dic59C2×D411yescharacteristic
171C22×Dic59C2×D411yescharacteristic
172C22×Dic59C2×D411yescharacteristic
173C22×Dic59C2×D411yescharacteristic
174C2×D236—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236C22×C412yes—
180C2×C4×D59—42no—
181C2×C4×D59—42no—
182C2×C4×D59—42no—
183C2×C8×C59—28no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59C2×D412yes—
189C2×C8×C59#4112yes—
190C4⋊C4×C59—24no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59C22×C412yes—
197C22⋊C4×C59—24no—
198C22⋊C4×C59—42no—
199C22⋊Dic59—42no—
200#11745671—28no—
201(C2×D59)⋊C4—24no—
202(C2×D59)⋊C4—42no—
203(C2×D59)⋊C4—42no—
204(C2×D59)⋊C4—42no—
205C4⋊Dic59—21no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—42no—
211C4⋊Dic59—42no—
212C4⋊Dic59C22×C412yes—
213Dic59⋊C4—42no—
214C4×Dic59—21no—
215C4×Dic59—21no—
216C4×Dic59—22no—
217C4×Dic59—22no—
218C4×Dic59—42no—
219C4×Dic59—42no—
220C4×Dic59—42no—
221C4×Dic59C2×D412yes—
222C4×Dic59#4112yes—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—28no—
226C2×C59⋊C8C22×C412yes—
227C2×C59⋊C8C22×C412yes—
228C2×C59⋊C8C2×D412yes—
229C2×C59⋊C8#4112yes—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59C4×D412yes—
235C23×C59C2×SD1612yes—
236C23×C59#13512yes—
237C23×C59C22×D411yescharacteristic
238C22×D59—22no—
239C22×D59—41no—
240C22×D59—41no—
241C22×D59—41no—
242C22×D59—41no—
243C22×D59—41no—
244C22×D59—41no—
245Q8×C59—22no—
246Q8×C59—22no—
247Q8×C59—41no—
248Q8×C59—41no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59C4×D412yes—
268C2×C4×C59C23×C411yescharacteristic
269C2×C4×C59C22×D411yescharacteristic
270C2×C4×C59C2×#4111yescharacteristic
271C2×C4×C59C2×#4111yescharacteristic
272C2×C4×C59C2×#4111yescharacteristic
273C2×C4×C59C2×#4111yescharacteristic
274C22⋊D59—48no—
275C2×Dic59—28no—
276C2×Dic59—21no—
277C2×Dic59—21no—
278C2×Dic59—21no—
279C2×Dic59—21no—
280C2×Dic59—21no—
281C2×Dic59—21no—
282C2×Dic59—28no—
283C2×Dic59—22no—
284C2×Dic59—41no—
285C2×Dic59—41no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59#12112yes—
293C2×Dic59#12112yes—
294C2×Dic59C2×SD1612yes—
295C2×Dic59C2×SD1612yes—
296C2×Dic59#13512yes—
297C2×Dic59#13512yes—
298D236—22no—
299D236—22no—
300D236—41no—
301D236—41no—
302C4×D59—84no—
303C8×C59—22no—
304C8×C59—22no—
305C59⋊C8—22no—
306C59⋊C8C4×D414yescomplemented
307C4×#465—591nomaximal, Sylow
308C22×C59—22no—
309C22×C59—22no—
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59C4×SD1614yescomplemented
315C22×C59C2×C4×D411yescharacteristic
316C22×C59C2×#12111yescharacteristic
317C22×C59#53211yescharacteristic
318C22×C59C22×SD1611yescharacteristic
319C22×C59C2×#13511yescharacteristic
320C22×C59C2×#13511yescharacteristic
321C22×C59C2×#13511yescharacteristic
322C2×D59—42no—
323C2×D59—42no—
324C2×D59—42no—
325C2×D59—81no—
326C2×D59—81no—
327C2×D59—81no—
328C2×D59—81no—
329C4×C59—22no—
330C4×C59—42no—
331C4×C59—42no—
332C4×C59—81no—
333C4×C59—81no—
334C4×C59C2×C4×D411yescharacteristic
335C4×C59C4×#4111yescharacteristic
336C4×C59#52511yescharacteristic
337C4×C59#52911yescharacteristic
338Dic59—22no—
339Dic59—22no—
340Dic59—22no—
341Dic59—42no—
342Dic59—81no—
343Dic59—81no—
344Dic59#46514yescomplemented
345C2×#465—591no—
346C2×C4×SD16—591no—
347C22×C4×C8—591no—
348C4×C22⋊Q8—591no—
349C4×#121—591no—
350#1968—591no—
351#1941—591no—
352#1934—591no—
353#1933—591no—
354#1893—591no—
355#1892D5911yescharacteristic, complemented
356#1807—591no—
357C4×#106—591no—
358C4×#103—591no—
359C4×#102—591no—
360C2×C59—24no—
361C2×C59C4×#12111yescharacteristic
362C2×C59C2×C4×SD1611yescharacteristic
363C2×C59C4×#13511yescharacteristic
364C2×C59C2×#46511yescharacteristic
365C2×C59#305011yescharacteristic
366C2×C59#316711yescharacteristic
367C2×C59#316811yescharacteristic
368D59—82no—
369C22×SD16—591no—
370C23×C8—591no—
371C23×C8C2×D5911yescharacteristic
372C2×C22⋊Q8C2×D5911yescharacteristic
373C2×#121—591no—
374C2×C4×Q8—591no—
375C2×C4×D4—591no—
376C2×C4×D4—1181no—
377C22×C42—591no—
378#465—598no—
379C4×SD16—1184no—
380C2×#106—591no—
381C2×#106—591no—
382C2×#106—591no—
383C2×#103—591no—
384C2×#103C2×D5911yescharacteristic
385C2×#103C2×D5911yescharacteristic
386C2×#102—591no—
387C2×#102—591no—
388C2×#102—591no—
389C2×C4×C8—591no—
390C2×C4×C8—591no—
391C2×C4×C8—591no—
392C2×C4×C8—591no—
393C2×C4×C8—1184no—
394#391—591no—
395#390—591no—
396#389—591no—
397#389—591no—
398#388—1181no—
399#387—1181no—
400#386—1181no—
401#385—1181no—
402#380—591no—
403#380C2×D5911yescharacteristic
404C4×C4⋊C4—591no—
405C4×C4⋊C4—591no—
406C4×C4⋊C4—1181no—
407C4×C22⋊C4—1181no—
408C4×C22⋊C4—1181no—
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#340C2×D5911yescharacteristic
414#340C2×D5911yescharacteristic
415C59C4×#46511yescharacteristic, complemented, Sylow
416C22×Q8C22×D5911yescharacteristic
417C22×D4—591no—
418C22×D4—1181no—
419C23×C4—591no—
420C23×C4—591no—
421C23×C4—1181no—
422C23×C4C22×D5911yescharacteristic
423C2×SD16—594no—
424C2×SD16—1182no—
425C2×SD16—1182no—
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—22no—
429C22×C8—591no—
430C22×C8—594no—
431C22×C8—591no—
432C22×C8—1182no—
433C22×C8—1182no—
434C22×C8C22×D5911yescharacteristic
435C22×C8C22×D5911yescharacteristic
436C22⋊Q8—22no—
437C22⋊Q8C4×D5914yescomplemented
438#121—594no—
439#121—1182no—
440C4×Q8—1182no—
441C4×Q8—1182no—
442C4×D4—1182no—
443C4×D4—1182no—
444C4×D4—2364no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—591no—
447C2×C4⋊C4—591no—
448C2×C4⋊C4—591no—
449C2×C4⋊C4—1181no—
450C2×C4⋊C4—1181no—
451C2×C4⋊C4—1181no—
452C2×C4⋊C4C22×D5911yescharacteristic
453C2×C4⋊C4C22×D5911yescharacteristic
454C2×C4⋊C4C22×D5911yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4—1181no—
459C2×C22⋊C4—1181no—
460C2×C22⋊C4—1181no—
461C2×C22⋊C4—1181no—
462C2×C42—591no—
463C2×C42—591no—
464C2×C42—591no—
465C2×C42—591no—
466C2×C42—1182no—
467C2×C42—1182no—
468C2×C42—1181no—
469C2×C42—1181no—
470C2×C42—1181no—
471#106—594no—
472#106—1182no—
473#106—1182no—
474#103—22no—
475#103—22no—
476#103—594no—
477#102—594no—
478#102—1182no—
479#102—1182no—
480C4×C8—594no—
481C4×C8—1182no—
482C4×C8—1182no—
483C4×C8—1182no—
484#95—21no—
485#95—1181no—
486#95—1181no—
487#95—1181no—
488#95—1181no—
489#95—1181no—
490#95—1181no—
491#95—1181no—
492C24—1181no—
493C24D4×D5911yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D5912yes—
500C2×D4—592no—
501C2×D4—1184no—
502C2×D4—1181no—
503C2×D4—1181no—
504C2×D4—1181no—
505C2×D4—1181no—
506C2×D4—1181no—
507C2×D4—2362no—
508C2×D4—2362no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—591no—
518C22×C4—594no—
519C22×C4—591no—
520C22×C4—591no—
521C22×C4—591no—
522C22×C4—1182no—
523C22×C4—1182no—
524C22×C4—1182no—
525C22×C4—1182no—
526C22×C4—1182no—
527C22×C4—1181no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4—2362no—
531C22×C4—2362no—
532C22×C4—2362no—
533C22×C4C2×C4×D5912yes—
534C22×C4D4×D5911yescharacteristic
535C22×C4#1174568712yes—
536C22×C4C23×D5911yescharacteristic
537SD16—1188no—
538C2×C8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—592no—
544C2×C8—592no—
545C2×C8—592no—
546C2×C8—592no—
547C2×C8—1188no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8D4×D5912yes—
551C2×C8#1174568712yes—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—592no—
559C4⋊C4—1181no—
560C4⋊C4—1181no—
561C4⋊C4—1181no—
562C4⋊C4—1181no—
563C4⋊C4—1181no—
564C4⋊C4—2362no—
565C4⋊C4—2362no—
566C4⋊C4—2362no—
567C4⋊C4C2×C4×D5912yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—1184no—
571C22⋊C4—2362no—
572C22⋊C4—2362no—
573C22⋊C4—2362no—
574C22⋊C4—2362no—
575C42—592no—
576C42—592no—
577C42—1182no—
578C42—1182no—
579C42—1181no—
580C42—1181no—
581C42—2362no—
582C42—2362no—
583C42—2362no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—1182no—
589C23—2361no—
590C23—2361no—
591C23—2361no—
592C23—2361no—
593C23—2361no—
594C23—2361no—
595C23(C22⋊D59)⋊C412yes—
596C23SD16×D5912yes—
597C23#1427375012yes—
598C23C2×D4×D5911yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—1182no—
604D4—1182no—
605D4—2368no—
606D4—2361no—
607D4—2361no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—592no—
627C2×C4—592no—
628C2×C4—592no—
629C2×C4—592no—
630C2×C4—592no—
631C2×C4—592no—
632C2×C4—1188no—
633C2×C4—1188no—
634C2×C4—1181no—
635C2×C4—1181no—
636C2×C4—1181no—
637C2×C4—1181no—
638C2×C4—1181no—
639C2×C4—1181no—
640C2×C4—1182no—
641C2×C4—4724no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4(C22⋊D59)⋊C412yes—
651C2×C4C22×C4×D5911yescharacteristic
652C2×C4C2×D4×D5911yescharacteristic
653C2×C4#41×D5911yescharacteristic
654C2×C4#41×D5911yescharacteristic
655C2×C4C2×#1174568711yescharacteristic
656C2×C4C2×#1174568711yescharacteristic
657C8—22no—
658C8—22no—
659C8—594no—
660C8—1182no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—4721no—
668C22—4721no—
669C22—4721no—
670C22—4721no—
671C22—2362no—
672C22—2362no—
673C22—2362no—
674C22#1683748714yescomplemented
675C22C2×(C22⋊D59)⋊C411yescharacteristic
676C22#121×D5911yescharacteristic
677C22#1683794711yescharacteristic
678C22C2×SD16×D5911yescharacteristic
679C22#135×D5911yescharacteristic
680C22#135×D5911yescharacteristic
681C22C2×#1427375011yescharacteristic
682C4—22no—
683C4—42no—
684C4—42no—
685C4—81no—
686C4—81no—
687C4—594no—
688C4—1182no—
689C4—1182no—
690C4—1182no—
691C4—4721no—
692C4—4721no—
693C4—2362no—
694C4C4×D4×D5911yescharacteristic
695C4C4×#1174568711yescharacteristic
696C4#1683790811yescharacteristic
697C4#1683792911yescharacteristic
698C2—24no—
699C2—4722no—
700C2#2142660611yescharacteristic
701C2C2×#1683748711yescharacteristic
702C2#2143286411yescharacteristic
703C2#465×D5911yescharacteristic
704C2#2143367911yescharacteristic
705C2#2143465011yescharacteristic
706C2#2143466711yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1892C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenter#1892D59
hypocenterC59C4×#465
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C2×#16837487C2semidirect
3. C22×C8×Dic59C2semidirect
4. C22⋊Q8×Dic59C2semidirect
6. #21424947C2semidirect
7. #21424823C2semidirect
8. #21424780C2semidirect
9. #21424769C2semidirect
11. #21424119C2semidirect
12. #21423984C2semidirect
13. #103×Dic59C2semidirect
14. #21423910C2semidirect
15. C59×#1892C2semidirect
23. #16837633C4semidirect
69. C2×#11745671C2×C4semidirect
72. C22×C59⋊C8C2×C4semidirect
104. #14273658C2×C4semidirect
105. #14273651C2×C4semidirect
108. #14273647C2×C4semidirect
112. C8×Dic59D4semidirect
128. C22⋊Q8×C59C2×C4semidirect
169. C22×Dic59SD16semidirect
306. C59⋊C8C4×D4semidirect
314. C22×C59C4×SD16semidirect
344. Dic59#465semidirect
355. #1892D59semidirect
415. C59C4×#465semidirect
437. C22⋊Q8C4×D59semidirect
674. C22#16837487semidirect

Maximal subgroups

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

subgroupindex
C2×#168376332
C2×#168374872
C22×C8×Dic592
C22⋊Q8×Dic592
#214266022
#214249472
#214248232
#214247802
#214247692
#214245242
#214241192
#214239842
#103×Dic592
#214239102
C59×#18922
C4×#46559