Finite Group Databasebeta

← #28609022

Subgroups — #28609022

Order 15104.

1086 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×#16837557C211yesmaximal, characteristic
2C2×#16837507C211yesmaximal, characteristic, complemented
3C22×#14273650C211yesmaximal, characteristic
4C22⋊C4×Dic118C211yesmaximal, characteristic
5#21424966C211yesmaximal, characteristic, complemented
6#21424785C211yesmaximal, characteristic, complemented
7#21424730C211yesmaximal, characteristic, complemented
8#21424520C211yesmaximal, characteristic
9#21424440C211yesmaximal, characteristic, complemented
10#21424437C211yesmaximal, characteristic, complemented
11#21424363C211yesmaximal, characteristic, complemented
12#21424289C211yesmaximal, characteristic
13#21423929C211yesmaximal, characteristic, complemented
14#21423874C211yesmaximal, characteristic
15C59×#2360C211yesmaximal, characteristic
16C23×Dic118C2211yescharacteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×C4×Dic118C2211yescharacteristic
21C2×C4×Dic118C2211yescharacteristic
22#16837557C418yescomplemented
23#16837507—24no—
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273650—24no—
29C2×#14273650C2211yescharacteristic
30C2×#14273650C2211yescharacteristic
31C2×#14273650C2211yescharacteristic
32C2×#14273650C2211yescharacteristic
33C2×#14273650C2211yescharacteristic
34C2×#14273650C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38#16837308C2211yescharacteristic
39#16837308C2211yescharacteristic
40#16837306—21no—
41#16837306—21no—
42#16837262C2211yescharacteristic
43#16837260—21no—
44C22⋊C4×Dic59—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C2×C22⋊Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C59×#391C2211yescharacteristic
55C59×#389—21no—
56C59×#389C2211yescharacteristic
57C59×#387—21no—
58C59×#385—21no—
59C4×C4⋊C4×C59C2211yescharacteristic
60C4×C22⋊C4×C59—21no—
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×Dic118—22no—
63C22×Dic118—22no—
64C22×Dic118—21no—
65C22×Dic118—22no—
66C22×Dic118—41no—
67C22×Dic118—41no—
68C22×Dic118C2×C414yes—
69C22×Dic118C2311yescharacteristic
70C22×Dic118C2311yescharacteristic
71C23×Dic59—21no—
72C2×#11745672—22no—
73C2×#11745672—22no—
74C2×#11745672—41no—
75C2×#11745672—41no—
76C2×#11745672C2×C414yescomplemented
77C2×#11745672C2×C414yescomplemented
78C22×C59⋊C8—22no—
79C22×C59⋊C8—22no—
80C22×C59⋊C8—41no—
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C4×Dic118—22no—
86C4×Dic118—22no—
87C4×Dic118—41no—
88C4×Dic118—41no—
89C2×C4⋊Dic59C2311yescharacteristic
90C2×C4⋊Dic59C2311yescharacteristic
91C2×Dic59⋊C4—21no—
92C2×Dic59⋊C4—21no—
93C2×C22⋊Dic59—21no—
94C2×C4×Dic59—21no—
95C2×C4×Dic59—21no—
96#14273658—22no—
97#14273658—41no—
98#14273651—22no—
99#14273651—41no—
100#14273650—22no—
101#14273650—22no—
102#14273650—22no—
103#14273650C2×C414yescomplemented
104#14273650C2×C414yescomplemented
105#14273650D414yes—
106C22⋊(C59⋊C8)C2×C414yes—
107#14273638—22no—
108#14273638—41no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C22×Q8×C59C2311yescharacteristic
115C23×C4×C59—21no—
116C23×C4×C59C2311yescharacteristic
117C22⋊Q8×C59—22no—
118C22⋊Q8×C59C2×C414yes—
119C4×Q8×C59—22no—
120C4×Q8×C59—41no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—22no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—41no—
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C22⋊C4×C59D411yescharacteristic
133C2×C42×C59—21no—
134C2×C42×C59—21no—
135C2×C42×C59C2311yescharacteristic
136C2×C42×C59C2311yescharacteristic
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141#95×C59D411yescharacteristic
142#95×C59D411yescharacteristic
143C24×C59C2×D411yescharacteristic
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59C22×C412yes—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—42no—
159C22×C4×C59—42no—
160C22×C4×C59—81no—
161C22×C4×C59C22×C412yes—
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59#4112yes—
168C22×C4×C59C2411yescharacteristic
169C22×Dic59—21no—
170C22×Dic59—24no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—42no—
175C22×Dic59—42no—
176C2×Dic118—21no—
177C2×Dic118—21no—
178C2×Dic118—21no—
179C2×Dic118—21no—
180C2×Dic118—21no—
181C2×Dic118—21no—
182C2×Dic118—21no—
183C2×Dic118—28no—
184C2×Dic118—24no—
185C2×Dic118—21no—
186C2×Dic118—44no—
187C2×Dic118—44no—
188C2×Dic118—44no—
189C2×Dic118—42no—
190C2×Dic118—42no—
191C2×Dic118C22×C412yes—
192C2×Dic118C22×C412yes—
193C2×Dic118C2×D412yes—
194C2×Dic118#4112yes—
195C4⋊C4×C59—24no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—42no—
201C4⋊C4×C59—42no—
202C4⋊C4×C59—81no—
203C4⋊C4×C59C22×C412yes—
204C4⋊C4×C59C2×D412yes—
205C22⋊C4×C59—24no—
206C22⋊C4×C59—22no—
207C22⋊C4×C59—22no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—21no—
212C42×C59—42no—
213C42×C59—81no—
214C22⋊Dic59—42no—
215#11745672—28no—
216#11745672—44no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221Dic59⋊C4—42no—
222Dic59⋊C4—42no—
223C4×Dic59—42no—
224C4×Dic59—42no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
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—44no—
235C2×C59⋊C8C22×C412yes—
236C2×C59⋊C8C22×C412yes—
237C2×C59⋊C8C2×D412yes—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59C4×D412yes—
243C23×C59#13712yes—
244C23×C59#13712yes—
245C23×C59C22×D411yescharacteristic
246Q8×C59—22no—
247Q8×C59—22no—
248Q8×C59—41no—
249Q8×C59—41no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—22no—
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—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
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×C59—84no—
281C2×C4×C59C4×D412yes—
282C2×C4×C59C23×C411yescharacteristic
283C2×C4×C59C22×D411yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C59H(5,𝔽2)11yescharacteristic
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—48no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301Dic118—22no—
302Dic118—22no—
303Dic118—22no—
304Dic118—22no—
305Dic118—22no—
306Dic118—48no—
307Dic118—41no—
308Dic118—41no—
309Dic118C4×D414yes—
310C59⋊C8—22no—
311C59⋊C8—22no—
312C59⋊C8—22no—
313C59⋊C8—41no—
314#22859—591nomaximal, Sylow
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—22no—
321C22×C59#44114yescomplemented
322C22×C59C2×C4×D411yescharacteristic
323C22×C59D4211yescharacteristic
324C22×C59#54611yescharacteristic
325C22×C59C2×#13711yescharacteristic
326C22×C59C2×#13711yescharacteristic
327C22×C59#57711yescharacteristic
328C22×C59#57811yescharacteristic
329C4×C59—22no—
330C4×C59—42no—
331C4×C59—42no—
332C4×C59—41no—
333C4×C59—42no—
334C4×C59—41no—
335C4×C59—41no—
336C4×C59—41no—
337C4×C59—81no—
338C4×C59C2×C4×D411yescharacteristic
339C4×C59#51811yescharacteristic
340C4×C59#54611yescharacteristic
341C4×C59#55111yescharacteristic
342Dic59—24no—
343Dic59—42no—
344Dic59—81no—
345Dic59—81no—
346C2×#451—591no—
347C2×#441—591no—
348C22×#103—591no—
349#2360D5911yescharacteristic
350Q8×C22⋊C4—591no—
351#1971—591no—
352#1935—591no—
353#1927—591no—
354#1892—591no—
355#1878—591no—
356#1878—591no—
357#1865—591no—
358#1853—591no—
359#1763—591no—
360#1752—591no—
361C2×C59—24no—
362C2×C59#235811yescharacteristic
363C2×C59C2×#44111yescharacteristic
364C2×C59#294711yescharacteristic
365C2×C59#326611yescharacteristic
366C2×C59#327011yescharacteristic
367C2×C59#331211yescharacteristic
368C2×C59#331611yescharacteristic
369C23×Q8—591no—
370C22×Q16—591no—
371C22×Q16—591no—
372C23×C8—591no—
373C2×C22⋊Q8C2×D5911yescharacteristic
374C2×C4×Q8—591no—
375C2×C4×Q8—591no—
376C2×C4×Q8C2×D5911yescharacteristic
377C22×C4⋊C4C2×D5911yescharacteristic
378#451—598no—
379#441—1184no—
380C2×#106—591no—
381C2×#106—591no—
382C2×#103—591no—
383C2×#103—591no—
384C2×#103—591no—
385C2×#103—591no—
386C2×#103—591no—
387C2×#103—591no—
388C2×#103—591no—
389C2×#103—591no—
390C2×#103—1184no—
391C2×C22⋊C8—591no—
392C2×#97—591no—
393C2×#97—591no—
394#391—591no—
395#391—591no—
396#391—1181no—
397#391—1181no—
398#391C2×D5911yescharacteristic
399#389—21no—
400#389C2×D5911yescharacteristic
401#387—21no—
402#385—21no—
403#380—591no—
404#380—1181no—
405C4×C4⋊C4C2×D5911yescharacteristic
406C4×C22⋊C4—21no—
407C4×C22⋊C4—1181no—
408C4×C22⋊C4C2×D5911yescharacteristic
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#336—591no—
414#336—591no—
415C59#2285911yescharacteristic, complemented, Sylow
416C22×Q8—594no—
417C22×Q8—591no—
418C22×Q8—591no—
419C22×Q8—1182no—
420C22×Q8—1182no—
421C22×Q8—1182no—
422C22×Q8—1181no—
423C22×Q8—2361no—
424C22×Q8—2361no—
425C22×Q8C22×D5911yescharacteristic
426C23×C4—21no—
427C23×C4—1181no—
428C23×C4C22×D5911yescharacteristic
429C2×Q16—594no—
430C2×Q16—594no—
431C2×Q16—1182no—
432C2×Q16—1182no—
433C2×Q16—2361no—
434C2×Q16—2361no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—591no—
438C22×C8—591no—
439C22×C8—1182no—
440C22×C8—1182no—
441C22×C8—2361no—
442C22⋊Q8—22no—
443C22⋊Q8C4×D5914yes—
444C4×Q8—22no—
445C4×Q8—41no—
446C4×Q8—1182no—
447C4×Q8—1182no—
448C4×Q8—2361no—
449C4×Q8—2361no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4—1181no—
459C2×C4⋊C4—1181no—
460C2×C4⋊C4C22×D5911yescharacteristic
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—1181no—
465C2×C22⋊C4C22⋊D5911yescharacteristic
466C2×C22⋊C4C22⋊D5911yescharacteristic
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—1181no—
470C2×C42—1181no—
471C2×C42C22×D5911yescharacteristic
472C2×C42C22×D5911yescharacteristic
473#106—1182no—
474#106—2361no—
475#103—594no—
476#103—594no—
477#103—594no—
478#103—1182no—
479#103—1182no—
480#103—1182no—
481#103—1182no—
482#103—2361no—
483C22⋊C8—594no—
484#97—1182no—
485#97—2361no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—1181no—
491#95—1181no—
492#95—1181no—
493#95—1181no—
494#95—1181no—
495#95C22⋊D5911yescharacteristic
496#95C22⋊D5911yescharacteristic
497C24C2×C22⋊D5911yescharacteristic
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—592no—
504C2×Q8—592no—
505C2×Q8—592no—
506C2×Q8—592no—
507C2×Q8—1188no—
508C2×Q8—1184no—
509C2×Q8—1181no—
510C2×Q8—1181no—
511C2×Q8—1181no—
512C2×Q8—1181no—
513C2×Q8—1181no—
514C2×Q8—1181no—
515C2×Q8—1181no—
516C2×Q8—1181no—
517C2×Q8—2362no—
518C2×Q8—2362no—
519C2×Q8—2364no—
520C2×Q8—2364no—
521C2×Q8—2364no—
522C2×Q8C2×C4×D5912yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—81no—
534C22×C4—1181no—
535C22×C4—1184no—
536C22×C4—1181no—
537C22×C4—1181no—
538C22×C4—1181no—
539C22×C4—2362no—
540C22×C4—2362no—
541C22×C4C2×C4×D5912yes—
542C22×C4#1174568512yes—
543C22×C4C2×C22⋊D5911yescharacteristic
544C22×C4C2×C22⋊D5911yescharacteristic
545C22×C4C2×C22⋊D5911yescharacteristic
546C22×C4C2×C22⋊D5911yescharacteristic
547C22×C4C2×C22⋊D5911yescharacteristic
548C22×C4C23×D5911yescharacteristic
549Q16—1188no—
550Q16—2364no—
551C2×C8—592no—
552C2×C8—592no—
553C2×C8—592no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—2364no—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—81no—
572C4⋊C4—1181no—
573C4⋊C4—1181no—
574C4⋊C4—1181no—
575C4⋊C4—1181no—
576C4⋊C4—2362no—
577C4⋊C4—2362no—
578C4⋊C4C2×C4×D5912yes—
579C4⋊C4D4×D5912yes—
580C22⋊C4—24no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—2362no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C42—81no—
590C42—2362no—
591C42—2362no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C4×C22⋊D5912yes—
597C23#1427375712yes—
598C23#1427375812yes—
599C23C22×C22⋊D5911yescharacteristic
600Q8—22no—
601Q8—22no—
602Q8—41no—
603Q8—41no—
604Q8—594no—
605Q8—1182no—
606Q8—1182no—
607Q8—1182no—
608Q8—1182no—
609Q8—1182no—
610Q8—2368no—
611Q8—2361no—
612Q8—2361no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—2368no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4C4×C22⋊D5912yes—
658C2×C4C22×C4×D5911yescharacteristic
659C2×C4C2×D4×D5911yescharacteristic
660C2×C4#41×D5911yescharacteristic
661C2×C4C2×#1174568511yescharacteristic
662C2×C4#1427377211yescharacteristic
663C2×C4#1427377311yescharacteristic
664C8—1182no—
665C8—1182no—
666C8—1182no—
667C8—2361no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22#1683750714yescomplemented
675C22C2×C4×C22⋊D5911yescharacteristic
676C22D4×C22⋊D5911yescharacteristic
677C22#1683804011yescharacteristic
678C22C2×#1427375711yescharacteristic
679C22C2×#1427375811yescharacteristic
680C22#1683821311yescharacteristic
681C22#1683821711yescharacteristic
682C4—22no—
683C4—41no—
684C4—41no—
685C4—42no—
686C4—42no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—81no—
691C4—1184no—
692C4—4721no—
693C4—4721no—
694C4—2362no—
695C4C4×D4×D5911yescharacteristic
696C4#1683787411yescharacteristic
697C4#1683804811yescharacteristic
698C4#1683808111yescharacteristic
699C2—24no—
700C2#2142707311yescharacteristic
701C2C2×#1683750711yescharacteristic
702C2#2143293511yescharacteristic
703C2#2143560211yescharacteristic
704C2#2143566711yescharacteristic
705C2#2143614111yescharacteristic
706C2#2143620111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2360C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
cosocleC22×C4×C59C24
hypercenter#2360D59
hypocenterC59#22859
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×#16837507C2semidirect
5. #21424966C2semidirect
6. #21424785C2semidirect
7. #21424730C2semidirect
9. #21424440C2semidirect
10. #21424437C2semidirect
11. #21424363C2semidirect
13. #21423929C2semidirect
22. #16837557C4semidirect
76. C2×#11745672C2×C4semidirect
77. C2×#11745672C2×C4semidirect
103. #14273650C2×C4semidirect
104. #14273650C2×C4semidirect
321. C22×C59#441semidirect
415. C59#22859semidirect
674. C22#16837507semidirect

Maximal subgroups

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

subgroupindex
C2×#168375572
C2×#168375072
C22×#142736502
C22⋊C4×Dic1182
#214249662
#214247852
#214247302
#214245202
#214244402
#214244372
#214243632
#214242892
#214239292
#214238742
C59×#23602
#2285959