Finite Group Databasebeta

← #28610345

Subgroups — #28610345

Order 15104.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432823C211yesmaximal, characteristic
2#21432754C211yesmaximal, characteristic, complemented
3#21424850C211yesmaximal, characteristic, complemented
4#21424802C211yesmaximal, characteristic, complemented
5#21424746C211yesmaximal, characteristic, complemented
6#21424697C211yesmaximal, characteristic, complemented
7#21424697C211yesmaximal, characteristic, complemented
8#21424545C211yesmaximal, characteristic
9#21424373C211yesmaximal, characteristic, complemented
10#21424303C211yesmaximal, characteristic, complemented
11#21423977C211yesmaximal, characteristic, complemented
12#21423943C211yesmaximal, characteristic, complemented
13#21423864C211yesmaximal, characteristic, complemented
14#21423805C211yesmaximal, characteristic, complemented
15C59×#3091C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19#16837480—21no—
20#16837474—21no—
21#16837474—21no—
22D4×C59⋊C8—21no—
23#16837463—21no—
24#16837463—21no—
25#16837459—21no—
26#16837455—21no—
27C2×#14273663C2211yescharacteristic
28C2×#14273663C2211yescharacteristic
29#16837429C2211yescharacteristic
30#16837429C2211yescharacteristic
31#16837429C2211yescharacteristic
32C2×#14273654C2211yescharacteristic
33C2×#14273654C2211yescharacteristic
34#16837369C2211yescharacteristic
35#16837366C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37#16837358C2211yescharacteristic
38#16837358C2211yescharacteristic
39#16837358C2211yescharacteristic
40C2×#14273637C2211yescharacteristic
41C2×C8×Dic59C2211yescharacteristic
42#16837167C2211yescharacteristic
43#16837167C2211yescharacteristic
44#16837161C2211yescharacteristic
45#16837161C2211yescharacteristic
46#16837161C2211yescharacteristic
47#16837161C2211yescharacteristic
48#16837161C2211yescharacteristic
49#16837161C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C59×#525C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C59×#485C411yescharacteristic, complemented
55C59×#485C411yescharacteristic, complemented
56C59×#484C411yescharacteristic, complemented
57C59×#483C411yescharacteristic, complemented
58C59×#482C411yescharacteristic, complemented
59C59×#482C411yescharacteristic, complemented
60C59×#481C411yescharacteristic, complemented
61C59×#480C411yescharacteristic, complemented
62C59×#427C2211yescharacteristic
63C59×#427C2211yescharacteristic
64C59×#416C2211yescharacteristic
65C59×#416C2211yescharacteristic
66C2×C22⋊C8×C59C2211yescharacteristic
67#14273734—22no—
68#14273734—41no—
69C2×#11745664—21no—
70C2×#11745664—21no—
71C2×#11745664—22no—
72C2×#11745664—41no—
73C2×#11745664C2311yescharacteristic
74C2×#11745664C2311yescharacteristic
75C2×#11745664C2311yescharacteristic
76C2×#11745664C2311yescharacteristic
77C22×C59⋊C8—21no—
78C22×C59⋊C8—21no—
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81#14273686—22no—
82#14273686—41no—
83C2×C4⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C4×Dic59C2311yescharacteristic
86C2×C4×Dic59C2311yescharacteristic
87#14273663—22no—
88#14273663—41no—
89C4⋊(C59⋊C8)—21no—
90C4⋊(C59⋊C8)—21no—
91C4⋊(C59⋊C8)—21no—
92C4⋊(C59⋊C8)—21no—
93C4⋊(C59⋊C8)—21no—
94C4⋊(C59⋊C8)—21no—
95#14273654—22no—
96#14273654—41no—
97C22⋊(C59⋊C8)—21no—
98C22⋊(C59⋊C8)—21no—
99C22⋊(C59⋊C8)—21no—
100C22⋊(C59⋊C8)—21no—
101C22⋊(C59⋊C8)D411yescharacteristic
102C22⋊(C59⋊C8)D411yescharacteristic
103C22⋊(C59⋊C8)D411yescharacteristic
104C22⋊(C59⋊C8)D411yescharacteristic
105#14273638—21no—
106#14273638—21no—
107#14273638—21no—
108#14273637—41no—
109C4×C59⋊C8—21no—
110C4×C59⋊C8—21no—
111C4×C59⋊C8—21no—
112C8×Dic59—22no—
113C2×#41×C59C2311yescharacteristic
114C23×C4×C59C2311yescharacteristic
115C22×C8×C59C2311yescharacteristic
116C22×C8×C59C2311yescharacteristic
117#123×C59—21no—
118C22⋊Q8×C59C2×C411yescharacteristic
119C22⋊Q8×C59C2×C411yescharacteristic
120#121×C59C2×C411yescharacteristic
121#121×C59C2×C411yescharacteristic
122#120×C59—21no—
123C4×D4×C59—21no—
124C4×D4×C59—21no—
125#117×C59—21no—
126#117×C59—21no—
127#117×C59C2×C411yescharacteristic
128#117×C59C2×C411yescharacteristic
129#117×C59C2311yescharacteristic
130#117×C59C2311yescharacteristic
131#117×C59C2311yescharacteristic
132C2×C4⋊C4×C59C2×C411yescharacteristic
133C2×C4⋊C4×C59C2×C411yescharacteristic
134C2×C22⋊C4×C59—21no—
135C2×C42×C59—21no—
136#107×C59C2×C411yescharacteristic
137#107×C59C2×C411yescharacteristic
138#107×C59C2×C411yescharacteristic
139#107×C59C2×C411yescharacteristic
140#106×C59C2×C411yescharacteristic
141#106×C59C2×C411yescharacteristic
142#106×C59C2×C411yescharacteristic
143#106×C59C2×C411yescharacteristic
144#103×C59C2×C411yescharacteristic
145#103×C59C2×C411yescharacteristic
146#103×C59C2×C411yescharacteristic
147#103×C59C2×C411yescharacteristic
148#102×C59C2×C411yescharacteristic
149#102×C59C2×C411yescharacteristic
150#102×C59C2×C411yescharacteristic
151#102×C59C2×C411yescharacteristic
152C22⋊C8×C59C2×C411yescharacteristic
153C22⋊C8×C59C2×C411yescharacteristic
154C22⋊C8×C59C2×C411yescharacteristic
155C22⋊C8×C59C2×C411yescharacteristic
156C24×C59#4111yescharacteristic
157#41×C59—21no—
158#41×C59—21no—
159#41×C59—21no—
160#41×C59—21no—
161C2×Q8×C59C22×C411yescharacteristic
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59C22×C411yescharacteristic
166C22×C4×C59—21no—
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×C59C22×C411yescharacteristic
174C22×C4×C59C22×C411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59#4111yescharacteristic
178C22×C4×C59C2411yescharacteristic
179C22×Dic59—21no—
180C22×Dic59—21no—
181C2×C8×C59—21no—
182C2×C8×C59—21no—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59C22×C411yescharacteristic
186C2×C8×C59C22×C411yescharacteristic
187C2×C8×C59C22×C411yescharacteristic
188C2×C8×C59C22×C411yescharacteristic
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59C22×C411yescharacteristic
194C4⋊C4×C59C22×C411yescharacteristic
195C4⋊C4×C59C22×C411yescharacteristic
196C4⋊C4×C59C22×C411yescharacteristic
197C4⋊C4×C59C22×C411yescharacteristic
198C4⋊C4×C59C22×C411yescharacteristic
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—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—21no—
212C42×C59—21no—
213C22⋊Dic59—42no—
214C4⋊Dic59—42no—
215C4×Dic59—21no—
216C4×Dic59—21no—
217C4×Dic59—21no—
218C4×Dic59#4112yes—
219#11745664—21no—
220#11745664—21no—
221#11745664—21no—
222#11745664—21no—
223#11745664—21no—
224#11745664—21no—
225#11745664—21no—
226#11745664—42no—
227#11745664—42no—
228#11745664#4112yes—
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—42no—
238C2×C59⋊C8—42no—
239C2×C59⋊C8C2×D411yescharacteristic
240C2×C59⋊C8C2×D411yescharacteristic
241C2×C59⋊C8C2×D411yescharacteristic
242C2×C59⋊C8C2×D411yescharacteristic
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59C4×D411yescharacteristic
249C23×C59C4×D411yescharacteristic
250C23×C59C2×#4111yescharacteristic
251Q8×C59—21no—
252Q8×C59—21no—
253D4×C59—21no—
254D4×C59—21no—
255D4×C59—42no—
256D4×C59—41no—
257D4×C59—41no—
258D4×C59—81no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—42no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—81no—
280C2×C4×C59C4×D411yescharacteristic
281C2×C4×C59C4×D411yescharacteristic
282C2×C4×C59C23×C411yescharacteristic
283C2×C4×C59C22×D411yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C592−1+411yescharacteristic
288C2×Dic59—22no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C8×C59—21no—
295C8×C59—21no—
296C8×C59—21no—
297C8×C59—21no—
298C59⋊C8—21no—
299C59⋊C8—21no—
300C59⋊C8—22no—
301C59⋊C8—21no—
302C59⋊C8—21no—
303C59⋊C8—41no—
304C59⋊C8—41no—
305C59⋊C8—41no—
306#22951—591nomaximal, Sylow
307C22×C59—21no—
308C22×C59—21no—
309C22×C59—21no—
310C22×C59—21no—
311C22×C59—21no—
312C22×C59—21no—
313C22×C59—21no—
314C22×C59—21no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—81no—
319C22×C59—81no—
320C22×C59C2×C4×D411yescharacteristic
321C22×C59#55111yescharacteristic
322C22×C59#55211yescharacteristic
323C4×C59—21no—
324C4×C59—21no—
325C4×C59—41no—
326C4×C59—41no—
327C4×C59—41no—
328C4×C59—41no—
329C4×C59—41no—
330C4×C59—41no—
331C4×C59—41no—
332C4×C59C4×#4111yescharacteristic
333C4×C59#52011yescharacteristic
334C4×C59#54611yescharacteristic
335C4×C59#54711yescharacteristic
336Dic59—42no—
337Dic59—81no—
338#3091D5911yescharacteristic
339#2933—591no—
340#2924—591no—
341#1946—591no—
342#1937—591no—
343#1929—591no—
344#1922—591no—
345#1922—591no—
346#1897—591no—
347#1866—591no—
348#1855—591no—
349#1772—591no—
350#1765—591no—
351#1750—591no—
352#1733—591no—
353C2×C59—21no—
354C2×C59—21no—
355C2×C59—41no—
356C2×C59—41no—
357C2×C59—81no—
358C2×C59#235911yescharacteristic
359C2×C59#295511yescharacteristic
360C2×C59#295711yescharacteristic
361C2×#131—591no—
362C22×M16—591no—
363#525C2×D5911yescharacteristic
364C2×#117—591no—
365C2×#117C2×D5911yescharacteristic
366#485Dic5911yescharacteristic, complemented
367#485Dic5911yescharacteristic, complemented
368#484Dic5911yescharacteristic, complemented
369#483Dic5911yescharacteristic, complemented
370#482Dic5911yescharacteristic, complemented
371#482Dic5911yescharacteristic, complemented
372#481Dic5911yescharacteristic, complemented
373#480Dic5911yescharacteristic, complemented
374#436—1181no—
375#435—1181no—
376#435—1181no—
377C8×D4—1181no—
378#433—1181no—
379#433—1181no—
380#432—1181no—
381#431—1181no—
382C2×#108—591no—
383C2×#108—591no—
384#427C2×D5911yescharacteristic
385#427C2×D5911yescharacteristic
386#424—591no—
387#424—591no—
388#424—591no—
389C2×#104—591no—
390C2×#104—591no—
391#416C2×D5911yescharacteristic
392#416C2×D5911yescharacteristic
393#408—591no—
394#407—591no—
395C2×C22⋊C8—591no—
396C2×C22⋊C8C2×D5911yescharacteristic
397#405—591no—
398#405—591no—
399#405—591no—
400C2×#97—591no—
401C2×C4×C8—591no—
402#341—591no—
403#341—591no—
404#339—591no—
405#339—591no—
406#339—591no—
407#339—591no—
408#339—591no—
409#339—591no—
410#336—591no—
411#336—591no—
412C59#2295111yescharacteristic, complemented, Sylow
413C2×#41C22×D5911yescharacteristic
414C23×C4C22×D5911yescharacteristic
415#131—1182no—
416#131—2361no—
417C2×M16—591no—
418C2×M16—591no—
419C2×M16—591no—
420C2×M16—591no—
421C2×M16—1181no—
422C2×M16—1181no—
423C2×M16—1182no—
424C2×M16—2361no—
425C22×C8—591no—
426C22×C8—591no—
427C22×C8—1181no—
428C22×C8—1181no—
429C22×C8C22×D5911yescharacteristic
430C22×C8C22×D5911yescharacteristic
431#123—21no—
432C22⋊Q8C2×Dic5911yescharacteristic
433C22⋊Q8C2×Dic5911yescharacteristic
434#121C2×Dic5911yescharacteristic
435#121C2×Dic5911yescharacteristic
436#120—21no—
437C4×D4—21no—
438C4×D4—21no—
439#117—21no—
440#117—21no—
441#117—1182no—
442#117—2361no—
443#117C2×Dic5911yescharacteristic
444#117C2×Dic5911yescharacteristic
445#117C22×D5911yescharacteristic
446#117C22×D5911yescharacteristic
447#117C22×D5911yescharacteristic
448C2×C4⋊C4—1181no—
449C2×C4⋊C4C2×Dic5911yescharacteristic
450C2×C4⋊C4C2×Dic5911yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—1181no—
453C2×C42—21no—
454C2×C42—591no—
455C2×C42—591no—
456#108—1182no—
457#108—2361no—
458#107C2×Dic5911yescharacteristic
459#107C2×Dic5911yescharacteristic
460#107C2×Dic5911yescharacteristic
461#107C2×Dic5911yescharacteristic
462#106C2×Dic5911yescharacteristic
463#106C2×Dic5911yescharacteristic
464#106C2×Dic5911yescharacteristic
465#106C2×Dic5911yescharacteristic
466C4⋊C8—1181no—
467C4⋊C8—1181no—
468C4⋊C8—1181no—
469C4⋊C8—1181no—
470C4⋊C8—1181no—
471C4⋊C8—1181no—
472#104—1182no—
473#104—2361no—
474#103C2×Dic5911yescharacteristic
475#103C2×Dic5911yescharacteristic
476#103C2×Dic5911yescharacteristic
477#103C2×Dic5911yescharacteristic
478#102C2×Dic5911yescharacteristic
479#102C2×Dic5911yescharacteristic
480#102C2×Dic5911yescharacteristic
481#102C2×Dic5911yescharacteristic
482C22⋊C8—591no—
483C22⋊C8—591no—
484C22⋊C8—591no—
485C22⋊C8—591no—
486C22⋊C8—1181no—
487C22⋊C8—1181no—
488C22⋊C8—1181no—
489C22⋊C8—1181no—
490C22⋊C8C2×Dic5911yescharacteristic
491C22⋊C8C2×Dic5911yescharacteristic
492C22⋊C8C2×Dic5911yescharacteristic
493C22⋊C8C2×Dic5911yescharacteristic
494#97—1181no—
495#97—1181no—
496#97—1181no—
497#97—2361no—
498C4×C8—1181no—
499C4×C8—1181no—
500C4×C8—1181no—
501C4×C8—1182no—
502C24#1174568711yescharacteristic
503#41—21no—
504#41—21no—
505#41—21no—
506#41—21no—
507C2×Q8C22×Dic5911yescharacteristic
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C22×Dic5911yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—1181no—
520C22×C4—1181no—
521C22×C4D4×D5911yescharacteristic
522C22×C4D4×D5911yescharacteristic
523C22×C4#1174568711yescharacteristic
524C22×C4C22×Dic5911yescharacteristic
525C22×C4C22×Dic5911yescharacteristic
526C22×C4C23×D5911yescharacteristic
527M16—592no—
528M16—1181no—
529M16—1181no—
530M16—1181no—
531M16—1181no—
532M16—1181no—
533M16—1181no—
534M16—1181no—
535M16—2362no—
536M16—2362no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—591no—
542C2×C8—591no—
543C2×C8—591no—
544C2×C8—591no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—2362no—
554C2×C8—2362no—
555C2×C8C22×Dic5911yescharacteristic
556C2×C8C22×Dic5911yescharacteristic
557C2×C8C22×Dic5911yescharacteristic
558C2×C8C22×Dic5911yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—2362no—
564C4⋊C4C22×Dic5911yescharacteristic
565C4⋊C4C22×Dic5911yescharacteristic
566C4⋊C4C22×Dic5911yescharacteristic
567C4⋊C4C22×Dic5911yescharacteristic
568C4⋊C4C22×Dic5911yescharacteristic
569C4⋊C4C22×Dic5911yescharacteristic
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—2362no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—592no—
586C42—1181no—
587C42—1181no—
588C42—1181no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—41no—
593C23—41no—
594C23D4×Dic5911yescharacteristic
595C23D4×Dic5911yescharacteristic
596C23C2×#1174568711yescharacteristic
597Q8—21no—
598Q8—21no—
599D4—21no—
600D4—21no—
601D4—42no—
602D4—41no—
603D4—41no—
604D4—81no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—81no—
626C2×C4—1182no—
627C2×C4—2361no—
628C2×C4—2361no—
629C2×C4—2361no—
630C2×C4—2361no—
631C2×C4—2361no—
632C2×C4D4×Dic5911yescharacteristic
633C2×C4D4×Dic5911yescharacteristic
634C2×C4C23×Dic5911yescharacteristic
635C2×C4C2×D4×D5911yescharacteristic
636C2×C4#41×D5911yescharacteristic
637C2×C4#41×D5911yescharacteristic
638C2×C4#1427377311yescharacteristic
639C2×C4#1427377411yescharacteristic
640C8—21no—
641C8—21no—
642C8—21no—
643C8—21no—
644C8—1181no—
645C8—1181no—
646C8—1182no—
647C8—1181no—
648C8—1181no—
649C8—2361no—
650C8—2361no—
651C8—2361no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—81no—
664C22—81no—
665C22C2×D4×Dic5911yescharacteristic
666C22#1683807511yescharacteristic
667C22#1683808911yescharacteristic
668C4—21no—
669C4—21no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—41no—
677C4—4721no—
678C4—2362no—
679C4#41×Dic5911yescharacteristic
680C4#1683788511yescharacteristic
681C4#1683804411yescharacteristic
682C4#1683805011yescharacteristic
683C2—21no—
684C2—21no—
685C2—41no—
686C2—41no—
687C2—81no—
688C2#2142709211yescharacteristic
689C2#2143299911yescharacteristic
690C2#2143301311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#3091C2
socleC22×C59C2×C4×D4
prime radicalC59×#525C22
cosocleC22×C4×C59C24
hypercenter#3091D59
hypocenterC59#22951
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. #21432754C2semidirect
3. #21424850C2semidirect
4. #21424802C2semidirect
5. #21424746C2semidirect
6. #21424697C2semidirect
7. #21424697C2semidirect
9. #21424373C2semidirect
10. #21424303C2semidirect
11. #21423977C2semidirect
12. #21423943C2semidirect
13. #21423864C2semidirect
14. #21423805C2semidirect
54. C59×#485C4semidirect
55. C59×#485C4semidirect
56. C59×#484C4semidirect
57. C59×#483C4semidirect
58. C59×#482C4semidirect
59. C59×#482C4semidirect
60. C59×#481C4semidirect
61. C59×#480C4semidirect
366. #485Dic59semidirect
367. #485Dic59semidirect
368. #484Dic59semidirect
369. #483Dic59semidirect
370. #482Dic59semidirect
371. #482Dic59semidirect
372. #481Dic59semidirect
373. #480Dic59semidirect
412. C59#22951semidirect

Maximal subgroups

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

subgroupindex
#214328232
#214327542
#214248502
#214248022
#214247462
#214246972
#214245452
#214243732
#214243032
#214239772
#214239432
#214238642
#214238052
C59×#30912
#2295159