Finite Group Databasebeta

← #28611312

Subgroups — #28611312

Order 15104.

1150 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837636C211yesmaximal, characteristic
2C2×#16837482C211yesmaximal, characteristic, complemented
3C22×#14273660C211yesmaximal, characteristic, complemented
4#21427116C211yesmaximal, characteristic, complemented
5#21427112C211yesmaximal, characteristic, complemented
6#21424959C211yesmaximal, characteristic, complemented
7#21424828C211yesmaximal, characteristic, complemented
8#21424719C211yesmaximal, characteristic, complemented
9#21424714C211yesmaximal, characteristic, complemented
10#21424411C211yesmaximal, characteristic, complemented
11#21424344C211yesmaximal, characteristic, complemented
12#21424341C211yesmaximal, characteristic, complemented
13#21423988C211yesmaximal, characteristic, complemented
14#21423870C211yesmaximal, characteristic, complemented
15C59×#1874C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×D4×Dic59—21no—
20C2×D4×Dic59C2211yescharacteristic
21C2×#14273689C2211yescharacteristic
22C2×C4×C22⋊D59—21no—
23C22×C4⋊Dic59C2211yescharacteristic
24#16837636C418yescomplemented
25#16837482—24no—
26C2×#14273660—24no—
27C2×#14273660C2211yescharacteristic
28C2×#14273660C2211yescharacteristic
29C2×#14273660C2211yescharacteristic
30C2×#14273660C2211yescharacteristic
31C2×#14273660C2211yescharacteristic
32C2×#14273649C2211yescharacteristic
33C2×#14273649C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C8×Dic59C2211yescharacteristic
37C2×C8×Dic59C2211yescharacteristic
38#16837305C2211yescharacteristic
39#16837303C2211yescharacteristic
40#16837301C2211yescharacteristic
41#16837298C2211yescharacteristic
42#16837295—21no—
43#16837292—21no—
44#16837282—21no—
45#16837281—21no—
46#16837277—21no—
47#16837273—21no—
48C4⋊C4×Dic59C2211yescharacteristic
49C4⋊C4×Dic59C2211yescharacteristic
50C4×C22⋊Dic59C2211yescharacteristic
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53#16837156C2211yescharacteristic
54#16837156C2211yescharacteristic
55C2×#121×C59C2211yescharacteristic
56C22×C4⋊C4×C59C2211yescharacteristic
57C2×#102×C59C2211yescharacteristic
58C2×#102×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C23×Dic59—21no—
65C23×Dic59—21no—
66C22×C4×D59—21no—
67C2×#11745669—22no—
68C2×#11745669—22no—
69C2×#11745669C2×C414yescomplemented
70C22×C59⋊C8—22no—
71C22×C59⋊C8—22no—
72C22×C59⋊C8C2×C414yescomplemented
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273701—22no—
76#14273701C2×C414yescomplemented
77D4×Dic59—22no—
78D4×Dic59—41no—
79D4×Dic59—44no—
80#14273689—22no—
81#14273689—41no—
82C4×C22⋊D59—44no—
83C2×C4⋊Dic59—22no—
84C2×C4⋊Dic59—21no—
85C2×C4⋊Dic59—21no—
86C2×C4⋊Dic59—41no—
87C2×C4⋊Dic59C2311yescharacteristic
88C2×C4⋊Dic59C2311yescharacteristic
89C2×C4⋊Dic59C2311yescharacteristic
90C2×Dic59⋊C4—21no—
91C2×C22⋊Dic59—21no—
92C2×C22⋊Dic59—21no—
93C2×C22⋊Dic59—21no—
94C2×C22⋊Dic59D411yescharacteristic
95C2×C22⋊Dic59D411yescharacteristic
96C2×(C2×D59)⋊C4—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C2×C4×Dic59—21no—
101C2×C4×Dic59—21no—
102C2×C4×Dic59C2311yescharacteristic
103C2×C4×Dic59C2311yescharacteristic
104#14273660—22no—
105#14273660—22no—
106#14273660—22no—
107#14273660C2×C414yescomplemented
108#14273660D414yescomplemented
109#14273649—22no—
110#14273649—41no—
111#14273648C2×C414yescomplemented
112#14273647C2×C414yescomplemented
113C8×Dic59—22no—
114C8×Dic59—22no—
115C59⋊#95—21no—
116C59⋊#95—21no—
117C59⋊#95—21no—
118C59⋊#95—21no—
119C59⋊#95D411yescharacteristic
120C59⋊#95D411yescharacteristic
121C22×D4×C59—21no—
122C22×D4×C59C2311yescharacteristic
123C23×C4×C59—21no—
124C23×C4×C59C2311yescharacteristic
125C22×C8×C59C2311yescharacteristic
126C22×C8×C59C2311yescharacteristic
127#121×C59—22no—
128#121×C59C2×C414yescomplemented
129C2×C4⋊C4×C59—22no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—41no—
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C22⋊C4×C59—21no—
136#102×C59—22no—
137#102×C59—41no—
138C22⋊C8×C59—22no—
139C24×C59—21no—
140C24×C59C2×D411yescharacteristic
141C23×D59—21no—
142C2×D4×C59—24no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—21no—
147C2×D4×C59—21no—
148C2×D4×C59—42no—
149C2×D4×C59—42no—
150C2×D4×C59C22×C412yes—
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×C59#4112yes—
164C22×C4×C59C2411yescharacteristic
165C2×C22⋊D59—24no—
166C2×C22⋊D59—42no—
167C2×C22⋊D59—42no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—42no—
172C22×Dic59—42no—
173C22×Dic59—42no—
174C22×Dic59—42no—
175C22×Dic59—81no—
176C22×Dic59—81no—
177C22×Dic59C2×D411yescharacteristic
178C22×Dic59C2×D411yescharacteristic
179C22×Dic59C2×D411yescharacteristic
180C22×Dic59C2×D411yescharacteristic
181C2×D236—21no—
182C2×D236—21no—
183C2×D236—21no—
184C2×D236—21no—
185C2×D236—21no—
186C2×D236C22×C412yes—
187C2×C4×D59—42no—
188C2×C4×D59—42no—
189C2×C4×D59—81no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C2×C8×C59—21no—
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—42no—
201C4⋊C4×C59C22×C412yes—
202C4⋊C4×C59C2×D412yes—
203C22⋊C4×C59—24no—
204C22⋊Dic59—22no—
205C22⋊Dic59—42no—
206C22⋊Dic59—42no—
207C22⋊Dic59—81no—
208C22⋊Dic59D814yescomplemented
209#11745669—28no—
210(C2×D59)⋊C4—24no—
211(C2×D59)⋊C4—42no—
212(C2×D59)⋊C4—42no—
213(C2×D59)⋊C4—81no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—42no—
219C4⋊Dic59—42no—
220C4⋊Dic59C22×C412yes—
221C4⋊Dic59C2×D412yes—
222Dic59⋊C4—42no—
223C4×Dic59—21no—
224C4×Dic59—21no—
225C4×Dic59—21no—
226C4×Dic59—21no—
227C4×Dic59—42no—
228C4×Dic59—42no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—28no—
232C2×C59⋊C8C22×C412yes—
233C2×C59⋊C8C22×C412yes—
234C2×C59⋊C8C2×D412yes—
235C2×C59⋊C8#4112yes—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—22no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59—41no—
247C23×C59C4×D412yes—
248C23×C59C2×D812yes—
249C23×C59#13512yes—
250C23×C59C22×D411yescharacteristic
251C22×D59—22no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
255C22×D59—41no—
256C22×D59—41no—
257C22×D59—41no—
258D4×C59—22no—
259D4×C59—22no—
260D4×C59—48no—
261D4×C59—41no—
262D4×C59—41no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
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—84no—
279C2×C4×C59C4×D412yes—
280C2×C4×C59C23×C411yescharacteristic
281C2×C4×C59C22×D411yescharacteristic
282C2×C4×C59C2×#4111yescharacteristic
283C2×C4×C59C2×#4111yescharacteristic
284C2×C4×C59H(5,𝔽2)11yescharacteristic
285C2×C4×C592−1+411yescharacteristic
286C22⋊D59—48no—
287C2×Dic59—21no—
288C2×Dic59—21no—
289C2×Dic59—21no—
290C2×Dic59—21no—
291C2×Dic59—22no—
292C2×Dic59—21no—
293C2×Dic59—22no—
294C2×Dic59—21no—
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—84no—
307C2×Dic59—84no—
308C2×Dic59C2×D812yes—
309C2×Dic59C2×D812yes—
310D236—22no—
311D236—22no—
312D236—41no—
313D236—41no—
314C4×D59—84no—
315C8×C59—41no—
316C8×C59—41no—
317C59⋊C8—22no—
318C59⋊C8C4×D414yescomplemented
319#23025—591nomaximal, Sylow
320C22×C59—22no—
321C22×C59—22no—
322C22×C59—22no—
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—42no—
327C22×C59—42no—
328C22×C59—42no—
329C22×C59—81no—
330C22×C59—81no—
331C22×C59—81no—
332C22×C59—81no—
333C22×C59C4×D814yescomplemented
334C22×C59C2×C4×D411yescharacteristic
335C22×C59D4211yescharacteristic
336C22×C59#54711yescharacteristic
337C22×C59C22×D811yescharacteristic
338C22×C59C2×#13511yescharacteristic
339C22×C59#57611yescharacteristic
340C22×C59#57811yescharacteristic
341C2×D59—42no—
342C2×D59—42no—
343C2×D59—42no—
344C2×D59—81no—
345C2×D59—81no—
346C2×D59—81no—
347C2×D59—81no—
348C4×C59—22no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—81no—
352C4×C59C2×C4×D411yescharacteristic
353C4×C59#52011yescharacteristic
354C4×C59#54811yescharacteristic
355C4×C59#55311yescharacteristic
356Dic59—22no—
357Dic59—22no—
358Dic59—41no—
359Dic59—42no—
360Dic59—42no—
361Dic59—41no—
362Dic59—81no—
363C2×#466—591no—
364C2×C4×D8—591no—
365C22×#107—591no—
366#2361—591no—
367#2361—591no—
368#1970—591no—
369#1942—591no—
370#1925—591no—
371#1925—591no—
372#1874—591no—
373#1874D5911yescharacteristic, complemented
374#1862—591no—
375#1862—591no—
376C4×#107—591no—
377C8×C22⋊C4—591no—
378C2×C59—24no—
379C2×C59—82no—
380C2×C59#236111yescharacteristic
381C2×C59C2×C4×D811yescharacteristic
382C2×C59#295111yescharacteristic
383C2×C59D4×D811yescharacteristic
384C2×C59#328511yescharacteristic
385C2×C59#333411yescharacteristic
386C2×C59#333911yescharacteristic
387D59—82no—
388C22×D8—591no—
389C23×C8—591no—
390C2×#121—591no—
391C2×#121C2×D5911yescharacteristic
392C2×C4×D4—591no—
393C2×C4×D4—591no—
394C2×C4×D4—1181no—
395C2×C4×D4—1181no—
396C22×C4⋊C4—591no—
397C22×C4⋊C4C2×D5911yescharacteristic
398#466—598no—
399C4×D8—1184no—
400C2×#107—591no—
401C2×#107—591no—
402C2×#107—591no—
403C2×#107—591no—
404C2×#107—591no—
405C2×#107—1184no—
406C2×#102—591no—
407C2×#102—591no—
408C2×#102—591no—
409C2×#102—591no—
410C2×#102C2×D5911yescharacteristic
411C2×#102C2×D5911yescharacteristic
412C2×C22⋊C8C2×D5911yescharacteristic
413C2×C4×C8—591no—
414C2×C4×C8—591no—
415#390—591no—
416#390—591no—
417#389—591no—
418#389—591no—
419#388—1181no—
420#388—1181no—
421#386—1181no—
422#386—1181no—
423#385—1181no—
424#385—1181no—
425C4×C4⋊C4—591no—
426C4×C4⋊C4—591no—
427C4×C22⋊C4—591no—
428#340—591no—
429#340—591no—
430#340C2×D5911yescharacteristic
431#340C2×D5911yescharacteristic
432#336—591no—
433#336—591no—
434C59#2302511yescharacteristic, complemented, Sylow
435C22×D4—21no—
436C22×D4—591no—
437C22×D4—1181no—
438C22×D4C22×D5911yescharacteristic
439C23×C4—21no—
440C23×C4—1181no—
441C23×C4—1181no—
442C23×C4—1181no—
443C23×C4C22×D5911yescharacteristic
444C2×D8—594no—
445C2×D8—1182no—
446C2×D8—1182no—
447C22×C8—591no—
448C22×C8—594no—
449C22×C8—591no—
450C22×C8—1182no—
451C22×C8—1182no—
452C22×C8C22×D5911yescharacteristic
453C22×C8C22×D5911yescharacteristic
454#121—22no—
455#121—594no—
456#121—1182no—
457#121C4×D5914yescomplemented
458C4×D4—1182no—
459C4×D4—1182no—
460C4×D4—2361no—
461C4×D4—2361no—
462C4×D4—2364no—
463C4×D4—2364no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—591no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—1182no—
471C2×C4⋊C4—1181no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—2361no—
475C2×C4⋊C4C22×D5911yescharacteristic
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—591no—
480C2×C22⋊C4—591no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4—1181no—
487C2×C22⋊C4—1181no—
488C2×C42—591no—
489C2×C42—591no—
490C2×C42—1181no—
491C2×C42—1181no—
492#107—594no—
493#107—594no—
494#107—1182no—
495#107—1182no—
496#107—1182no—
497#102—22no—
498#102—41no—
499#102—594no—
500#102—594no—
501#102—1182no—
502#102—2361no—
503C22⋊C8—22no—
504C4×C8—1182no—
505C4×C8—1182no—
506#95—591no—
507#95—591no—
508#95—1181no—
509#95—1181no—
510#95—1181no—
511#95—1181no—
512C24—21no—
513C24—1181no—
514C24D4×D5911yescharacteristic
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—592no—
524C2×D4—1184no—
525C2×D4—1181no—
526C2×D4—1181no—
527C2×D4—1181no—
528C2×D4—1181no—
529C2×D4—1181no—
530C2×D4—2362no—
531C2×D4—2362no—
532C2×D4C2×C4×D5912yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4—591no—
544C22×C4—591no—
545C22×C4—591no—
546C22×C4—591no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—1181no—
550C22×C4—4721no—
551C22×C4—4721no—
552C22×C4—4721no—
553C22×C4—2362no—
554C22×C4—2362no—
555C22×C4—2362no—
556C22×C4—2362no—
557C22×C4—2362no—
558C22×C4—2362no—
559C22×C4C2×C4×D5912yes—
560C22×C4D4×D5911yescharacteristic
561C22×C4#1174568712yes—
562C22×C4C23×D5911yescharacteristic
563D8—1188no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—592no—
571C2×C8—592no—
572C2×C8—592no—
573C2×C8—592no—
574C2×C8—1188no—
575C2×C8—1181no—
576C2×C8—1181no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—592no—
583C4⋊C4—592no—
584C4⋊C4—1181no—
585C4⋊C4—1181no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—2362no—
589C4⋊C4—2362no—
590C4⋊C4—2362no—
591C4⋊C4C2×C4×D5912yes—
592C4⋊C4D4×D5912yes—
593C22⋊C4—24no—
594C22⋊C4—594no—
595C22⋊C4—1182no—
596C22⋊C4—1184no—
597C22⋊C4—4721no—
598C22⋊C4—4721no—
599C22⋊C4—2362no—
600C22⋊C4—2362no—
601C22⋊C4—2362no—
602C22⋊C4—2362no—
603C42—1181no—
604C42—1181no—
605C42—1181no—
606C42—1181no—
607C42—2362no—
608C42—2362no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—1182no—
621C23—2361no—
622C23—2361no—
623C23—2361no—
624C23—2361no—
625C23—2361no—
626C23—2361no—
627C23(C22⋊D59)⋊C412yes—
628C23D8×D5912yes—
629C23#1427374812yes—
630C23C2×D4×D5911yescharacteristic
631D4—22no—
632D4—22no—
633D4—48no—
634D4—41no—
635D4—41no—
636D4—1182no—
637D4—1182no—
638D4—2368no—
639D4—2361no—
640D4—2361no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—84no—
657C2×C4—592no—
658C2×C4—592no—
659C2×C4—1181no—
660C2×C4—1181no—
661C2×C4—1181no—
662C2×C4—1181no—
663C2×C4—1181no—
664C2×C4—1181no—
665C2×C4—1181no—
666C2×C4—1181no—
667C2×C4—1181no—
668C2×C4—1182no—
669C2×C4—1181no—
670C2×C4—1182no—
671C2×C4—4724no—
672C2×C4—4724no—
673C2×C4—4724no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4(C22⋊D59)⋊C412yes—
682C2×C4C22×C4×D5911yescharacteristic
683C2×C4C2×D4×D5911yescharacteristic
684C2×C4#41×D5911yescharacteristic
685C2×C4C2×#1174568711yescharacteristic
686C2×C4#1427377211yescharacteristic
687C2×C4#1427377411yescharacteristic
688C8—41no—
689C8—41no—
690C8—594no—
691C8—1182no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—4721no—
706C22—4721no—
707C22—4721no—
708C22—4721no—
709C22—2362no—
710C22—2362no—
711C22—2362no—
712C22#1683748214yescomplemented
713C22C2×(C22⋊D59)⋊C411yescharacteristic
714C22#1683803411yescharacteristic
715C22#1683805011yescharacteristic
716C22C2×D8×D5911yescharacteristic
717C22C2×#1427374811yescharacteristic
718C22#1683820611yescharacteristic
719C22#1683821811yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—81no—
724C4—1182no—
725C4—1182no—
726C4—4721no—
727C4—2362no—
728C4—2361no—
729C4—2362no—
730C4—2361no—
731C4C4×D4×D5911yescharacteristic
732C4#1683788111yescharacteristic
733C4#1683805811yescharacteristic
734C4#1683809511yescharacteristic
735C2—24no—
736C2—82no—
737C2—4722no—
738C2#2142710711yescharacteristic
739C2C2×#1683748211yescharacteristic
740C2#2143296711yescharacteristic
741C2#2143576611yescharacteristic
742C2#2143583011yescharacteristic
743C2#2143643811yescharacteristic
744C2#2143649611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1874C2
socleC23×C59C22×D4
prime radicalC2×#16837636C2
cosocleC22×C4×C59C24
hypercenter#1874D59
hypocenterC59#23025
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#16837482C2semidirect
3. C22×#14273660C2semidirect
4. #21427116C2semidirect
5. #21427112C2semidirect
6. #21424959C2semidirect
7. #21424828C2semidirect
8. #21424719C2semidirect
9. #21424714C2semidirect
10. #21424411C2semidirect
11. #21424344C2semidirect
12. #21424341C2semidirect
13. #21423988C2semidirect
14. #21423870C2semidirect
15. C59×#1874C2semidirect
24. #16837636C4semidirect
69. C2×#11745669C2×C4semidirect
72. C22×C59⋊C8C2×C4semidirect
76. #14273701C2×C4semidirect
107. #14273660C2×C4semidirect
108. #14273660D4semidirect
111. #14273648C2×C4semidirect
112. #14273647C2×C4semidirect
128. #121×C59C2×C4semidirect
208. C22⋊Dic59D8semidirect
318. C59⋊C8C4×D4semidirect
333. C22×C59C4×D8semidirect
373. #1874D59semidirect
434. C59#23025semidirect
457. #121C4×D59semidirect
712. C22#16837482semidirect

Maximal subgroups

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

subgroupindex
C2×#168376362
C2×#168374822
C22×#142736602
#214271162
#214271122
#214249592
#214248282
#214247192
#214247142
#214244112
#214243442
#214243412
#214239882
#214238702
C59×#18742
#2302559