Finite Group Databasebeta

← #28606009

Subgroups — #28606009

Order 15104.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837406C211yesmaximal, characteristic
2C22⋊C4×D236C211yesmaximal, characteristic
3#21424792C211yesmaximal, characteristic, complemented
4#21424778C211yesmaximal, characteristic, complemented
5#21424723C211yesmaximal, characteristic, complemented
6#21424716C211yesmaximal, characteristic, complemented
7#21424356C211yesmaximal, characteristic, complemented
8#21424342C211yesmaximal, characteristic, complemented
9#21424191C211yesmaximal, characteristic, complemented
10#21424127C211yesmaximal, characteristic, complemented
11#21424026C211yesmaximal, characteristic
12#21423924C211yesmaximal, characteristic, complemented
13C4×#14273647C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#2346C211yesmaximal, characteristic, complemented
16C23×D236C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C22⋊C4×D59—21no—
21C2×#14273660C2211yescharacteristic, complemented
22C2×#14273658C2211yescharacteristic, complemented
23#16837406C418yescomplemented
24C2×#14273647C2211yescharacteristic
25C2×#14273647C2211yescharacteristic
26C2×#14273647C2211yescharacteristic
27C2×#14273647C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×#14273638C2211yescharacteristic, complemented
34C2×C4×C59⋊C8C2211yescharacteristic, complemented
35#16837304C2211yescharacteristic
36#16837304C2211yescharacteristic
37#16837280—21no—
38#16837280—21no—
39#16837262C2211yescharacteristic
40#16837257—21no—
41#16837164C2211yescharacteristic, complemented
42#16837164C2211yescharacteristic, complemented
43#16837164C2211yescharacteristic, complemented
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837157C2211yescharacteristic, complemented
48#16837157C2211yescharacteristic, complemented
49C2×#117×C59C2211yescharacteristic
50C59×#389C2211yescharacteristic, complemented
51C59×#389C2211yescharacteristic, complemented
52C59×#388—21no—
53C59×#388—21no—
54C59×#382—21no—
55C59×#380C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic, complemented
57C4×C4⋊C4×C59C2211yescharacteristic, complemented
58C4×C22⋊C4×C59C2211yescharacteristic
59C59×#376—21no—
60C24×D59—21no—
61C22×D236—22no—
62C22×D236—22no—
63C22×D236—21no—
64C22×D236—22no—
65C22×D236—41no—
66C22×D236—41no—
67C22×D236C2×C414yes—
68C22×D236C2311yescharacteristic
69C22×D236C2311yescharacteristic
70C22×C4×D59—21no—
71C22×C4×D59—21no—
72C2×#11745664—41no—
73C2×#11745664—41no—
74C2×#11745664C2×C414yescomplemented
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C4×D236—22no—
80C4×D236—22no—
81C4×D236—41no—
82C4×D236—41no—
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C22⋊Dic59—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C22⋊C4×D59—44no—
93#14273660—41no—
94#14273658—41no—
95#14273647—22no—
96#14273647—22no—
97#14273647—41no—
98#14273647—41no—
99#14273647C2×C414yes—
100#14273647C2×C414yes—
101#14273647C2×C414yescomplemented
102#14273647C2×C414yescomplemented
103C22⋊(C59⋊C8)—22no—
104#14273638—41no—
105C4×C59⋊C8—41no—
106C59⋊#95—21no—
107C23×C4×C59C2311yescharacteristic
108#117×C59—22no—
109#117×C59C2×C414yescomplemented
110C2×C4⋊C4×C59—21no—
111C2×C4⋊C4×C59—21no—
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C4⋊C4×C59C2311yescharacteristic
115C2×C4⋊C4×C59C2311yescharacteristic
116C2×C22⋊C4×C59—21no—
117C2×C22⋊C4×C59—21no—
118C2×C22⋊C4×C59D411yescharacteristic
119C2×C22⋊C4×C59D411yescharacteristic
120C2×C42×C59—21no—
121C2×C42×C59—21no—
122C2×C42×C59—21no—
123C2×C42×C59C2311yescharacteristic
124C2×C42×C59C2311yescharacteristic
125#95×C59—21no—
126#95×C59—21no—
127#95×C59—21no—
128#95×C59—21no—
129#95×C59—21no—
130#95×C59D411yescharacteristic
131#95×C59D411yescharacteristic
132C24×C59C2×D411yescharacteristic
133C23×D59—21no—
134C23×D59—21no—
135C23×D59—24no—
136C23×D59—42no—
137C23×D59—42no—
138C23×D59—42no—
139C23×D59—42no—
140C23×D59—81no—
141C23×D59—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×C59C22×C412yes—
151C22×C4×C59C2×D411yescharacteristic
152C22×C4×C59C2×D411yescharacteristic
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59#4112yes—
157C22×C4×C59C2411yescharacteristic
158C22×Dic59—21no—
159C22×Dic59—21no—
160C2×D236—21no—
161C2×D236—21no—
162C2×D236—21no—
163C2×D236—21no—
164C2×D236—21no—
165C2×D236—21no—
166C2×D236—21no—
167C2×D236—28no—
168C2×D236—24no—
169C2×D236—21no—
170C2×D236—44no—
171C2×D236—44no—
172C2×D236—44no—
173C2×D236—42no—
174C2×D236—42no—
175C2×D236C22×C412yes—
176C2×D236C22×C412yes—
177C2×D236#4112yes—
178C2×D236#4112yes—
179C2×C4×D59—42no—
180C2×C4×D59—42no—
181C2×C4×D59—42no—
182C2×C4×D59—42no—
183C2×C4×D59—81no—
184C2×C4×D59—81no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—81no—
192C4⋊C4×C59—81no—
193C4⋊C4×C59C22×C412yes—
194C4⋊C4×C59C22×C412yes—
195C22⋊C4×C59—24no—
196C22⋊C4×C59—22no—
197C22⋊C4×C59—41no—
198C22⋊C4×C59—81no—
199C42×C59—24no—
200C42×C59—21no—
201C42×C59—21no—
202C42×C59—21no—
203C42×C59—21no—
204C42×C59—42no—
205C42×C59—42no—
206C22⋊Dic59—42no—
207(C2×D59)⋊C4—42no—
208(C2×D59)⋊C4—42no—
209(C2×D59)⋊C4—42no—
210(C2×D59)⋊C4—42no—
211(C2×D59)⋊C4—81no—
212(C2×D59)⋊C4—81no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217#11745664—44no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
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⋊C8C22×C412yes—
229C2×C59⋊C8C22×C412yes—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59C4×D412yes—
237C23×C59C22×D411yescharacteristic
238C22×D59—22no—
239C22×D59—22no—
240C22×D59—22no—
241C22×D59—22no—
242C22×D59—48no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—48no—
248C22×D59—41no—
249C22×D59—41no—
250C22×D59—41no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—84no—
255C22×D59—84no—
256C22×D59—84no—
257C22×D59—84no—
258C22×D59—84no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
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—21no—
277C2×C4×C59—21no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59C4×D412yes—
289C2×C4×C59AGL(1,ℤ/8)12yes—
290C2×C4×C59C23×C411yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59H(5,𝔽2)11yescharacteristic
295C2×C4×C59H(5,𝔽2)11yescharacteristic
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302D236—22no—
303D236—22no—
304D236—22no—
305D236—22no—
306D236—22no—
307D236—48no—
308D236—41no—
309D236—41no—
310D236#11714yes—
311C4×D59—84no—
312C4×D59—84no—
313C59⋊C8—22no—
314C59⋊C8—22no—
315C59⋊C8—41no—
316C59⋊C8—41no—
317#22584—591nomaximal, Sylow
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—22no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—41no—
324C22×C59—41no—
325C22×C59C2×C4×D411yescharacteristic
326C22×C59#54611yescharacteristic
327C22×C59#54611yescharacteristic
328C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C59#57511yescharacteristic
330C22×C59#57611yescharacteristic
331C22×C59#57711yescharacteristic
332C2×D59—24no—
333C2×D59—42no—
334C2×D59—42no—
335C2×D59—42no—
336C2×D59—42no—
337C2×D59—42no—
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—42no—
341C2×D59—42no—
342C2×D59—816no—
343C2×D59—81no—
344C2×D59—81no—
345C2×D59—81no—
346C2×D59—81no—
347C4×C59—22no—
348C4×C59—22no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—41no—
352C4×C59—41no—
353C4×C59—41no—
354C4×C59—81no—
355C4×C59—81no—
356C4×C59C2×#11711yescharacteristic
357C4×C59#51811yescharacteristic
358C4×C59#55111yescharacteristic
359C4×C59#55111yescharacteristic
360Dic59—81no—
361Dic59—81no—
362C2×#418—591no—
363#2346D5911yescharacteristic, complemented
364D4×C22⋊C4—591no—
365#1936—591no—
366#1934—591no—
367#1926—591no—
368#1925—591no—
369#1864—591no—
370#1862—591no—
371#1825—591no—
372#1809—591no—
373#1786—591no—
374#1762—591no—
375C4×#102—591no—
376#1753—591no—
377C2×C59—42no—
378C2×C59#234211yescharacteristic
379C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
380C2×C59#294611yescharacteristic
381C2×C59#331011yescharacteristic
382C2×C59#331911yescharacteristic
383C2×C59#332311yescharacteristic
384C2×C59#332511yescharacteristic
385D59—44no—
386D59—82no—
387C23×D4—591no—
388C22×M16—591no—
389C2×C4×D4—591no—
390C2×C4×D4—591no—
391C2×#117C2×D5911yescharacteristic
392C22×C22⋊C4—1181no—
393C2×#107—591no—
394C2×#106—591no—
395#418—598no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102—591no—
399C2×#102—591no—
400C2×#102—591no—
401C2×#102—591no—
402C2×#102—591no—
403C2×#102—591no—
404C2×C22⋊C8—591no—
405C2×#97—591no—
406C2×C4×C8—591no—
407#390—591no—
408#390—591no—
409#389C2×D5911yescharacteristic, complemented
410#389C2×D5911yescharacteristic, complemented
411#388—21no—
412#388—21no—
413#386—1181no—
414#386—1181no—
415#382—21no—
416#380—591no—
417#380C2×D5911yescharacteristic
418#379—1181no—
419C4×C4⋊C4C2×D5911yescharacteristic, complemented
420C4×C4⋊C4C2×D5911yescharacteristic, complemented
421C4×C22⋊C4C2×D5911yescharacteristic
422#376—21no—
423#340—591no—
424#340—591no—
425#340—591no—
426#340—591no—
427#340—591no—
428#340—591no—
429#336—591no—
430#336—591no—
431C59#2258411yescharacteristic, complemented, Sylow
432C25—1181no—
433C22×D4—594no—
434C22×D4—591no—
435C22×D4—591no—
436C22×D4—1182no—
437C22×D4—1182no—
438C22×D4—1182no—
439C22×D4—1181no—
440C22×D4—2361no—
441C22×D4—2361no—
442C23×C4—1181no—
443C23×C4—1181no—
444C23×C4C22×D5911yescharacteristic
445C2×M16—594no—
446C2×M16—2361no—
447C2×M16—2361no—
448C22×C8—591no—
449C22×C8—591no—
450C22×C8—591no—
451C22×C8—591no—
452C4×D4—1182no—
453C4×D4—1182no—
454C4×D4—2361no—
455C4×D4—2361no—
456#117—22no—
457#117C4×D5914yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—591no—
461C2×C4⋊C4—591no—
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C4⋊C4C22×D5911yescharacteristic
464C2×C4⋊C4C22×D5911yescharacteristic
465C2×C4⋊C4C22×D5911yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—1181no—
469C2×C22⋊C4—1181no—
470C2×C22⋊C4—1181no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4—1181no—
473C2×C22⋊C4—1181no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4—2364no—
476C2×C22⋊C4C22⋊D5911yescharacteristic
477C2×C22⋊C4C22⋊D5911yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C22×D5911yescharacteristic
482C2×C42C22×D5911yescharacteristic
483#107—2361no—
484#106—2361no—
485#102—594no—
486#102—594no—
487#102—594no—
488#102—594no—
489#102—1182no—
490#102—1182no—
491#102—2361no—
492#102—2361no—
493C22⋊C8—1182no—
494#97—2361no—
495C4×C8—2361no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—1181no—
502#95C22⋊D5911yescharacteristic
503#95C22⋊D5911yescharacteristic
504C24—1181no—
505C24—1184no—
506C24—1181no—
507C24—4721no—
508C24—4721no—
509C24—2362no—
510C24—2362no—
511C24—2362no—
512C24—2362no—
513C24C2×C22⋊D5911yescharacteristic
514C2×D4—592no—
515C2×D4—592no—
516C2×D4—592no—
517C2×D4—592no—
518C2×D4—1188no—
519C2×D4—1184no—
520C2×D4—1181no—
521C2×D4—1181no—
522C2×D4—1181no—
523C2×D4—1181no—
524C2×D4—1181no—
525C2×D4—1181no—
526C2×D4—1181no—
527C2×D4—1181no—
528C2×D4—2364no—
529C2×D4—2364no—
530C2×D4—2364no—
531C2×D4—2362no—
532C2×D4—2362no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—1181no—
542C22×C4—1181no—
543C22×C4—4721no—
544C22×C4—4721no—
545C22×C4—2362no—
546C22×C4—2362no—
547C22×C4—2362no—
548C22×C4—2362no—
549C22×C4C2×C4×D5912yes—
550C22×C4#1174568512yes—
551C22×C4C2×C22⋊D5911yescharacteristic
552C22×C4C2×C22⋊D5911yescharacteristic
553C22×C4C2×C22⋊D5911yescharacteristic
554C22×C4C2×C22⋊D5911yescharacteristic
555C22×C4C2×C22⋊D5911yescharacteristic
556C22×C4C23×D5911yescharacteristic
557M16—2364no—
558C2×C8—592no—
559C2×C8—592no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—1181no—
565C2×C8—1181no—
566C2×C8—1181no—
567C2×C8—1181no—
568C2×C8—1181no—
569C2×C8—1181no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—1181no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4C2×C4×D5912yes—
583C4⋊C4C2×C4×D5912yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—81no—
588C22⋊C4—4721no—
589C22⋊C4—4721no—
590C22⋊C4—2362no—
591C22⋊C4—2362no—
592C22⋊C4—2362no—
593C22⋊C4—2362no—
594C22⋊C4—2362no—
595C42—24no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42—42no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—1182no—
609C23—1182no—
610C23—1182no—
611C23—1182no—
612C23—4724no—
613C23—4724no—
614C23—4724no—
615C23—4724no—
616C23—4724no—
617C23—2368no—
618C23—2368no—
619C23—2361no—
620C23—2361no—
621C23—2361no—
622C23—2361no—
623C23—2361no—
624C23—2361no—
625C23—2361no—
626C23—2361no—
627C23—2361no—
628C23—2361no—
629C23C4×C22⋊D5912yes—
630C23C22×C22⋊D5911yescharacteristic
631D4—594no—
632D4—1182no—
633D4—1182no—
634D4—1182no—
635D4—1182no—
636D4—1182no—
637D4—2368no—
638D4—2361no—
639D4—2361no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—4724no—
670C2×C4—4724no—
671C2×C4—2361no—
672C2×C4—2361no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4C4×C22⋊D5912yes—
678C2×C4#1427375212yes—
679C2×C4C22×C4×D5911yescharacteristic
680C2×C4#41×D5911yescharacteristic
681C2×C4#41×D5911yescharacteristic
682C2×C4C2×#1174568511yescharacteristic
683C2×C4#1427377311yescharacteristic
684C2×C4#1427377311yescharacteristic
685C8—1182no—
686C8—1182no—
687C8—2361no—
688C8—2361no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—1184no—
697C22—47216no—
698C22—4721no—
699C22—4721no—
700C22—4721no—
701C22—4721no—
702C22—2362no—
703C22—2362no—
704C22—2362no—
705C22—2362no—
706C22—2362no—
707C22—2362no—
708C22—2362no—
709C22—2362no—
710C22—2362no—
711C22C2×C4×C22⋊D5911yescharacteristic
712C22#1683804011yescharacteristic
713C22#1683804011yescharacteristic
714C22C2×#1427375211yescharacteristic
715C22#1683820011yescharacteristic
716C22#1683820511yescharacteristic
717C22#1683821011yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—41no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—4721no—
728C4—4721no—
729C4#117×D5911yescharacteristic
730C4#1683787611yescharacteristic
731C4#1683807611yescharacteristic
732C4#1683807611yescharacteristic
733C2—42no—
734C2—4722no—
735C2—2364no—
736C2#2142694611yescharacteristic
737C2C4×#1427375211yescharacteristic
738C2#2143292411yescharacteristic
739C2#2143611111yescharacteristic
740C2#2143624611yescharacteristic
741C2#2143630611yescharacteristic
742C2#2143633211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2346C2
socleC23×C59C22×D4
prime radicalC23×D236C22
cosocleC22×C4×C59C24
hypercenter#2346D59
hypocenterC59#22584
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2346

Complements

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

NH ≅ G/Ntype
3. #21424792C2semidirect
4. #21424778C2semidirect
5. #21424723C2semidirect
6. #21424716C2semidirect
7. #21424356C2semidirect
8. #21424342C2semidirect
9. #21424191C2semidirect
10. #21424127C2semidirect
12. #21423924C2semidirect
13. C4×#14273647C2semidirect
14. #21423880C2semidirect
15. C59×#2346C2semidirect
21. C2×#14273660C22semidirect
22. C2×#14273658C22semidirect
23. #16837406C4semidirect
33. C2×#14273638C22semidirect
34. C2×C4×C59⋊C8C22semidirect
41. #16837164C22semidirect
42. #16837164C22semidirect
43. #16837164C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837157C22semidirect
48. #16837157C22semidirect
50. C59×#389C22semidirect
51. C59×#389C22semidirect
56. C4×C4⋊C4×C59C22semidirect
57. C4×C4⋊C4×C59C22semidirect
74. C2×#11745664C2×C4semidirect
101. #14273647C2×C4semidirect
102. #14273647C2×C4semidirect
109. #117×C59C2×C4semidirect
363. #2346D59semidirect
409. #389C2×D59semidirect
410. #389C2×D59semidirect
419. C4×C4⋊C4C2×D59semidirect
420. C4×C4⋊C4C2×D59semidirect
431. C59#22584semidirect
457. #117C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168374062
C22⋊C4×D2362
#214247922
#214247782
#214247232
#214247162
#214243562
#214243422
#214241912
#214241272
#214240262
#214239242
C4×#142736472
#214238802
C59×#23462
#2258459