Finite Group Databasebeta

← #28645998

Subgroups — #28645998

Order 15104.

1004 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837684C211yesmaximal, characteristic, complemented
2C2×#16837401C211yesmaximal, characteristic
3#21426936C211yesmaximal, characteristic
4#21425630C211yesmaximal, characteristic, complemented
5#21425481C211yesmaximal, characteristic, complemented
6#21425467C211yesmaximal, characteristic, complemented
7#21425229C211yesmaximal, characteristic, complemented
8#21424363C211yesmaximal, characteristic, complemented
9#21424349C211yesmaximal, characteristic, complemented
10#21424289C211yesmaximal, characteristic, complemented
11#21424281C211yesmaximal, characteristic, complemented
12#21424127C211yesmaximal, characteristic, complemented
13#21424098C211yesmaximal, characteristic, complemented
14#21424034C211yesmaximal, characteristic
15C59×#2440C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C2×C4×Dic118C2211yescharacteristic
19C2×C4×Dic118C2211yescharacteristic
20#16837684—24no—
21C2×#14273660C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27#16837401—24no—
28C2×#14273650C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×#14273650C2211yescharacteristic
31C2×#14273650C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37#16837304C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837302—21no—
40#16837302—21no—
41#16837262C2211yescharacteristic
42#16837261—21no—
43#16837249—21no—
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C2×C4⋊Q8×C59C2211yescharacteristic
51C2×C22⋊Q8×C59—21no—
52C22×C4⋊C4×C59C2211yescharacteristic
53C59×#398—21no—
54C59×#395—21no—
55C59×#389C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#385—21no—
58C59×#384C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C4×C22⋊C4×C59C2211yescharacteristic
61C2×#11745685—22no—
62C2×#11745685—22no—
63C2×#11745685—22no—
64C2×#11745685—41no—
65C2×#11745685—41no—
66C2×#11745685Q814yescomplemented
67C22×Dic118C2311yescharacteristic
68C22×D236C2311yescharacteristic
69C22×C22⋊D59—21no—
70C22×C4×D59—21no—
71C2×#11745664—22no—
72C2×#11745664—22no—
73C2×#11745664—41no—
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C4×Dic118—22no—
79C4×Dic118—22no—
80C4×Dic118—41no—
81C4×Dic118—41no—
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×Dic59⋊C4—21no—
85C2×Dic59⋊C4—21no—
86C2×C22⋊Dic59—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×C4×Dic59—21no—
92C2×C4×Dic59—21no—
93#14273660—41no—
94#14273658—22no—
95#14273658—22no—
96#14273658—41no—
97C4⋊(C59⋊C8)—22no—
98C4⋊(C59⋊C8)—41no—
99#14273650—22no—
100#14273650—22no—
101#14273650—22no—
102#14273650D414yes—
103#14273647—22no—
104#14273647—22no—
105#14273647—41no—
106#14273647—41no—
107C22⋊(C59⋊C8)—22no—
108C59⋊#95—21no—
109C22×Q8×C59—21no—
110C23×C4×C59—21no—
111C23×C4×C59C2311yescharacteristic
112C4⋊Q8×C59—22no—
113C4⋊Q8×C59—41no—
114C22⋊Q8×C59—44no—
115C2×C4⋊C4×C59—22no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—41no—
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59D411yescharacteristic
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C42×C59C2311yescharacteristic
131C2×C42×C59C2311yescharacteristic
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59D411yescharacteristic
136#95×C59D411yescharacteristic
137C24×C59C2×D411yescharacteristic
138C23×D59—21no—
139C2×Q8×C59—42no—
140C2×Q8×C59—42no—
141C2×Q8×C59—81no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—42no—
151C22×C4×C59—42no—
152C22×C4×C59—81no—
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×Q812yes—
159C22×C4×C59#4112yes—
160C22×C4×C59C2411yescharacteristic
161C2×C22⋊D59—24no—
162C2×C22⋊D59—42no—
163C2×C22⋊D59—42no—
164C22×Dic59—21no—
165C22×Dic59—21no—
166C22×Dic59—21no—
167#11745685—28no—
168#11745685—44no—
169#11745685—44no—
170#11745685—44no—
171C2×D236—21no—
172C2×D236—21no—
173C2×D236—21no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236C2×Q812yes—
177C2×C4×D59—24no—
178C2×C4×D59—42no—
179C2×C4×D59—42no—
180C2×Dic118—21no—
181C2×Dic118—21no—
182C2×Dic118—21no—
183C2×Dic118C2×D412yes—
184C2×Dic118C2×Q812yes—
185C2×Dic118#4112yes—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—42no—
194C4⋊C4×C59—42no—
195C4⋊C4×C59—42no—
196C4⋊C4×C59—42no—
197C4⋊C4×C59—42no—
198C4⋊C4×C59—81no—
199C4⋊C4×C59C2×D412yes—
200C22⋊C4×C59—22no—
201C22⋊C4×C59—22no—
202C22⋊C4×C59—42no—
203C42×C59—21no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—21no—
207C22⋊Dic59—81no—
208(C2×D59)⋊C4—42no—
209(C2×D59)⋊C4—42no—
210(C2×D59)⋊C4—81no—
211(C2×D59)⋊C4—81no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216Dic59⋊C4—42no—
217Dic59⋊C4—42no—
218C4×Dic59—42no—
219C4×Dic59—42no—
220#11745664—44no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
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⋊C8C2×D412yes—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59C22⋊Q812yes—
240C23×C59C22×D411yescharacteristic
241C22×D59—22no—
242C22×D59—41no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248Q8×C59—84no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
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—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
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—84no—
278C2×C4×C59C22⋊Q812yes—
279C2×C4×C59AGL(1,ℤ/8)12yes—
280C2×C4×C59#13712yes—
281C2×C4×C59C22×D411yescharacteristic
282C2×C4×C59C22×Q811yescharacteristic
283C2×C4×C59C2×#4111yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59H(5,𝔽2)11yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C22⋊D59—48no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297D236—22no—
298D236—22no—
299D236—41no—
300D236—41no—
301C4×D59—48no—
302Dic118—22no—
303Dic118—22no—
304Dic118—22no—
305Dic118C22⋊Q814yescomplemented
306C59⋊C8—22no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309C59⋊C8—41no—
310#25967—591nomaximal, Sylow
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—41no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59C2×C22⋊Q811yescharacteristic
319C22×C59D4211yescharacteristic
320C22×C59#54611yescharacteristic
321C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C59C2×#13711yescharacteristic
323C22×C59#57711yescharacteristic
324C22×C59#57711yescharacteristic
325C2×D59—42no—
326C2×D59—42no—
327C2×D59—42no—
328C2×D59—81no—
329C2×D59—81no—
330C2×D59—81no—
331C2×D59—81no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—41no—
336C4×C59—42no—
337C4×C59—41no—
338C4×C59—81no—
339C4×C59—81no—
340C4×C59—81no—
341C4×C59C2×C22⋊Q811yescharacteristic
342C4×C59#54311yescharacteristic
343C4×C59#54611yescharacteristic
344C4×C59#55111yescharacteristic
345Dic59—24no—
346Dic59—81no—
347Dic59—81no—
348C2×#475—591no—
349C2×#417—591no—
350#2440D5911yescharacteristic, complemented
351#2341—591no—
352#2094—591no—
353#2067—591no—
354#2065—591no—
355#2023—591no—
356#1865—591no—
357#1863—591no—
358#1853—591no—
359#1851—591no—
360#1809—591no—
361#1803—591no—
362#1788—591no—
363C2×C59—42no—
364C2×C59#243711yescharacteristic
365C2×C59#307911yescharacteristic
366C2×C59#308411yescharacteristic
367C2×C59#326511yescharacteristic
368C2×C59#327811yescharacteristic
369C2×C59#331611yescharacteristic
370C2×C59#333211yescharacteristic
371D59—82no—
372C22×#41—591no—
373C22×M16—591no—
374C2×C4⋊Q8C2×D5911yescharacteristic
375C2×C22⋊Q8—21no—
376C2×C4×Q8—591no—
377C2×C4×Q8—591no—
378C22×C4⋊C4C2×D5911yescharacteristic
379#475—1184no—
380C2×#107—591no—
381C2×#106—591no—
382C2×#106—591no—
383C2×#106—591no—
384C2×C4⋊C8—591no—
385C2×C4⋊C8—591no—
386#417—1184no—
387C2×#103—591no—
388C2×#103—591no—
389C2×#103—591no—
390C2×#103—591no—
391C2×#102—591no—
392C2×#102—591no—
393C2×#102—591no—
394C2×#102—591no—
395C2×C22⋊C8—591no—
396#398—21no—
397#395—21no—
398#390—591no—
399#390—591no—
400#390—1181no—
401#390—1181no—
402#389C2×D5911yescharacteristic
403#389C2×D5911yescharacteristic
404#385—21no—
405#384C2×D5911yescharacteristic
406#380—591no—
407#380—1181no—
408#380C2×D5911yescharacteristic
409C4×C22⋊C4—1181no—
410C4×C22⋊C4C2×D5911yescharacteristic
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#336—591no—
416#336—591no—
417C59#2596711yescharacteristic, complemented, Sylow
418C2×#41—594no—
419C2×#41—1182no—
420C2×#41—1182no—
421C2×#41—1182no—
422C2×#41—2361no—
423C2×#41—2361no—
424C22×Q8—21no—
425C22×Q8—591no—
426C22×D4—591no—
427C22×D4—1181no—
428C23×C4—21no—
429C23×C4—1181no—
430C23×C4C22×D5911yescharacteristic
431C2×M16—1182no—
432C2×M16—1182no—
433C2×M16—2361no—
434C22×C8—591no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—591no—
438C4⋊Q8—22no—
439C4⋊Q8—41no—
440C22⋊Q8—44no—
441C4×Q8—1182no—
442C4×Q8—1182no—
443C4×Q8—2361no—
444C4×Q8—2361no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—1181no—
456C2×C4⋊C4—1181no—
457C2×C4⋊C4C22×D5911yescharacteristic
458C2×C4⋊C4C22×D5911yescharacteristic
459C2×C4⋊C4C22×D5911yescharacteristic
460C2×C4⋊C4C22×D5911yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—1181no—
463C2×C22⋊C4—1181no—
464C2×C22⋊C4—1181no—
465C2×C22⋊C4—1181no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4C22⋊D5911yescharacteristic
468C2×C22⋊C4C22⋊D5911yescharacteristic
469C2×C42—1181no—
470C2×C42—1181no—
471C2×C42C22×D5911yescharacteristic
472C2×C42C22×D5911yescharacteristic
473#107—2361no—
474#106—1182no—
475#106—1182no—
476#106—2361no—
477C4⋊C8—1182no—
478C4⋊C8—2361no—
479#103—594no—
480#103—1182no—
481#103—1182no—
482#103—1182no—
483#102—1182no—
484#102—1182no—
485#102—2361no—
486#102—2361no—
487C22⋊C8—1182no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—1181no—
492#95C22⋊D5911yescharacteristic
493#95C22⋊D5911yescharacteristic
494C24—1181no—
495C24C2×C22⋊D5911yescharacteristic
496#41—1188no—
497#41—2364no—
498#41—2364no—
499#41—2364no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—81no—
503C2×Q8—592no—
504C2×Q8—592no—
505C2×Q8—592no—
506C2×Q8—1181no—
507C2×Q8—1181no—
508C2×Q8—1181no—
509C2×D4—592no—
510C2×D4—1184no—
511C2×D4—1181no—
512C2×D4—1181no—
513C2×D4—1181no—
514C2×D4—1181no—
515C2×D4—1181no—
516C2×D4—2362no—
517C2×D4—2362no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—1181no—
530C22×C4—1184no—
531C22×C4—1181no—
532C22×C4—1181no—
533C22×C4—2362no—
534C22×C4—2362no—
535C22×C4Q8×D5912yes—
536C22×C4#1174568912yes—
537C22×C4C2×C22⋊D5911yescharacteristic
538C22×C4C2×C22⋊D5911yescharacteristic
539C22×C4C2×C22⋊D5911yescharacteristic
540C22×C4C2×C22⋊D5911yescharacteristic
541C22×C4C2×C22⋊D5911yescharacteristic
542C22×C4C23×D5911yescharacteristic
543M16—2364no—
544C2×C8—592no—
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—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—81no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—1181no—
572C4⋊C4—1181no—
573C4⋊C4—2362no—
574C4⋊C4—2362no—
575C4⋊C4D4×D5912yes—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—4721no—
580C22⋊C4—4721no—
581C22⋊C4—4721no—
582C22⋊C4—2362no—
583C22⋊C4—2362no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—2362no—
589C42—2362no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—1182no—
597C23—2361no—
598C23—2361no—
599C23—2361no—
600C23—2361no—
601C23—2361no—
602C23—2361no—
603C23#1427370312yes—
604C23C22×C22⋊D5911yescharacteristic
605Q8—84no—
606Q8—594no—
607Q8—1182no—
608Q8—1182no—
609Q8—1182no—
610D4—1182no—
611D4—1182no—
612D4—2368no—
613D4—2361no—
614D4—2361no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—41no—
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—2368no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4#1427370312yes—
655C2×C4#1427375312yes—
656C2×C4#1427375812yes—
657C2×C4C2×D4×D5911yescharacteristic
658C2×C4C2×Q8×D5911yescharacteristic
659C2×C4#41×D5911yescharacteristic
660C2×C4C2×#1174568911yescharacteristic
661C2×C4#1427377211yescharacteristic
662C2×C4#1427377311yescharacteristic
663C8—1182no—
664C8—2361no—
665C8—2361no—
666C8—2361no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—4721no—
675C22—4721no—
676C22—4721no—
677C22—4721no—
678C22—2362no—
679C22—2362no—
680C22—2362no—
681C22C2×#1427370311yescharacteristic
682C22D4×C22⋊D5911yescharacteristic
683C22#1683804011yescharacteristic
684C22C2×#1427375311yescharacteristic
685C22C2×#1427375811yescharacteristic
686C22#1683821011yescharacteristic
687C22#1683821311yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—1184no—
698C4—4721no—
699C4—4721no—
700C4C22⋊Q8×D5911yescharacteristic
701C4#1683802711yescharacteristic
702C4#1683804311yescharacteristic
703C4#1683807911yescharacteristic
704C2—42no—
705C2—4722no—
706C2#2142775911yescharacteristic
707C2#2143390511yescharacteristic
708C2#2143395411yescharacteristic
709C2#2143558711yescharacteristic
710C2#2143575811yescharacteristic
711C2#2143620111yescharacteristic
712C2#2143641711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2440C2
socleC23×C59C22×D4
prime radicalC22×#11745685C22
hypercenter#2440D59
hypocenterC59#25967
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#16837684C2semidirect
4. #21425630C2semidirect
5. #21425481C2semidirect
6. #21425467C2semidirect
7. #21425229C2semidirect
8. #21424363C2semidirect
9. #21424349C2semidirect
10. #21424289C2semidirect
11. #21424281C2semidirect
12. #21424127C2semidirect
13. #21424098C2semidirect
15. C59×#2440C2semidirect
66. C2×#11745685Q8semidirect
305. Dic118C22⋊Q8semidirect
350. #2440D59semidirect
417. C59#25967semidirect

Maximal subgroups

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

subgroupindex
C2×#168376842
C2×#168374012
#214269362
#214256302
#214254812
#214254672
#214252292
#214243632
#214243492
#214242892
#214242812
#214241272
#214240982
#214240342
C59×#24402
#2596759