Finite Group Databasebeta

← #28611086

Subgroups — #28611086

Order 15104.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837594C211yesmaximal, characteristic
2C2×#16837512C211yesmaximal, characteristic, complemented
3C2×C4×#11745669C211yesmaximal, characteristic, complemented
4#21427007C211yesmaximal, characteristic, complemented
5#21424921C211yesmaximal, characteristic, complemented
6#21424864C211yesmaximal, characteristic, complemented
7#21424796C211yesmaximal, characteristic, complemented
8#21424782C211yesmaximal, characteristic, complemented
9#21424447C211yesmaximal, characteristic, complemented
10#21424447C211yesmaximal, characteristic, complemented
11#21424357C211yesmaximal, characteristic, complemented
12#21424343C211yesmaximal, characteristic, complemented
13#21423971C211yesmaximal, characteristic, complemented
14#21423924C211yesmaximal, characteristic, complemented
15C59×#2366C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21#16837594C418yescomplemented
22#16837512—24no—
23C4×#11745669—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273638C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic
38#16837300C2211yescharacteristic
39#16837300C2211yescharacteristic
40#16837273—21no—
41#16837273—21no—
42#16837268C2211yescharacteristic
43#16837261—21no—
44#95×D59—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C2×#127×C59C2211yescharacteristic
52C2×C4×D4×C59—21no—
53C2×C4×D4×C59C2211yescharacteristic
54C2×C4×D4×C59C2211yescharacteristic
55C59×#390—21no—
56C59×#390C2211yescharacteristic
57C59×#390C2211yescharacteristic
58C59×#386—21no—
59C59×#386—21no—
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C4⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C4×D59—21no—
64C22×C4×D59—21no—
65C22×C4×D59—21no—
66C2×#11745669—22no—
67C2×#11745669—22no—
68C2×#11745669—22no—
69C2×#11745669—22no—
70C2×#11745669C2×C414yescomplemented
71C2×#11745669C2×C414yescomplemented
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C4×D236—22no—
77C4×D236—22no—
78C4×D236—22no—
79C4×D236—41no—
80C4×D236—41no—
81C4×D236C2×C414yescomplemented
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×Dic59⋊C4—21no—
86C2×Dic59⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90#14273660—22no—
91#14273658—22no—
92C4⋊(C59⋊C8)C2×C414yescomplemented
93#14273648—22no—
94#14273648—22no—
95#14273648—41no—
96#14273648—41no—
97#14273648C2×C414yescomplemented
98#14273648C2×C414yescomplemented
99#14273647—22no—
100#14273647D414yescomplemented
101#14273638—22no—
102#14273638—22no—
103C4×C59⋊C8—22no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×D4×C59—21no—
109C22×D4×C59—21no—
110C22×D4×C59C2311yescharacteristic
111C22×D4×C59C2311yescharacteristic
112C23×C4×C59—21no—
113C23×C4×C59—21no—
114#127×C59—22no—
115#127×C59C2×C414yescomplemented
116C4×D4×C59—22no—
117C4×D4×C59—22no—
118C4×D4×C59—41no—
119C4×D4×C59—41no—
120C4×D4×C59—44no—
121C2×C4⋊C4×C59D411yescharacteristic
122C2×C4⋊C4×C59D411yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C42×C59—21no—
132C2×C42×C59C2311yescharacteristic
133C2×C42×C59C2311yescharacteristic
134C2×C42×C59C2311yescharacteristic
135#95×C59—21no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
138C24×C59—21no—
139C24×C59—21no—
140C23×D59—21no—
141C2×D4×C59—24no—
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—21no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—42no—
154C2×D4×C59—42no—
155C2×D4×C59—81no—
156C2×D4×C59—81no—
157C2×D4×C59C22×C412yes—
158C2×D4×C59C22×C412yes—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—42no—
162C22×C4×C59—42no—
163C22×C4×C59—42no—
164C22×C4×C59—42no—
165C22×C4×C59—81no—
166C22×C4×C59—81no—
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2411yescharacteristic
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236C22×C412yes—
181C2×D236C2×D412yes—
182C2×D236#4112yes—
183C2×C4×D59—24no—
184C2×C4×D59—42no—
185C2×C4×D59—42no—
186C2×C4×D59—42no—
187C2×C4×D59—42no—
188C2×C4×D59—81no—
189C2×C4×D59—81no—
190C2×C4×D59—81no—
191C2×C4×D59—81no—
192C4⋊C4×C59—22no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—41no—
197C4⋊C4×C59C2×D412yes—
198C22⋊C4×C59—42no—
199C22⋊C4×C59—42no—
200C22⋊C4×C59—42no—
201C22⋊C4×C59—42no—
202C22⋊C4×C59—81no—
203C22⋊C4×C59—81no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—21no—
208C42×C59—42no—
209C42×C59C22×C412yes—
210C42×C59#4112yes—
211#11745669—28no—
212#11745669—28no—
213(C2×D59)⋊C4—24no—
214(C2×D59)⋊C4—42no—
215(C2×D59)⋊C4—42no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59C22×C412yes—
222Dic59⋊C4—81no—
223Dic59⋊C4—81no—
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⋊C8—21no—
233C2×C59⋊C8C22×C412yes—
234C2×C59⋊C8C22×C412yes—
235C2×C59⋊C8C2×D412yes—
236C23×C59—22no—
237C23×C59—22no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59—41no—
249C23×C59—41no—
250C23×C59C22×D411yescharacteristic
251C22×D59—22no—
252C22×D59—22no—
253C22×D59—22no—
254C22×D59—41no—
255C22×D59—41no—
256C22×D59—41no—
257C22×D59—41no—
258D4×C59—22no—
259D4×C59—22no—
260D4×C59—22no—
261D4×C59—22no—
262D4×C59—48no—
263D4×C59—41no—
264D4×C59—41no—
265D4×C59—41no—
266D4×C59—41no—
267D4×C59—84no—
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—21no—
277C2×C4×C59—22no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—84no—
290C2×C4×C59—84no—
291C2×C4×C59C4×D412yes—
292C2×C4×C59C4×D412yes—
293C2×C4×C59AGL(1,ℤ/8)12yes—
294C2×C4×C59C23×C411yescharacteristic
295C2×C4×C59C22×D411yescharacteristic
296C2×C4×C59C2×#4111yescharacteristic
297C2×C4×C59C2×#4111yescharacteristic
298C2×C4×C59H(5,𝔽2)11yescharacteristic
299C2×C4×C592−1+411yescharacteristic
300C2×Dic59—22no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309D236—22no—
310D236—22no—
311D236—22no—
312D236C4×D414yescomplemented
313C4×D59—84no—
314C4×D59—84no—
315C4×D59—84no—
316C59⋊C8—22no—
317C59⋊C8—22no—
318C59⋊C8—22no—
319C59⋊C8—41no—
320#23008—591nomaximal, Sylow
321C22×C59—42no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—42no—
325C22×C59—42no—
326C22×C59—42no—
327C22×C59—81no—
328C22×C59—81no—
329C22×C59—81no—
330C22×C59—81no—
331C22×C59—81no—
332C22×C59—81no—
333C22×C59—81no—
334C22×C59—81no—
335C22×C59C2×C4×D411yescharacteristic
336C22×C59D4211yescharacteristic
337C22×C59#54811yescharacteristic
338C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C59#57511yescharacteristic
340C22×C59#57611yescharacteristic
341C22×C59#57611yescharacteristic
342C2×D59—24no—
343C2×D59—42no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—42no—
347C2×D59—42no—
348C2×D59—42no—
349C4×C59—22no—
350C4×C59—22no—
351C4×C59—22no—
352C4×C59—41no—
353C4×C59—42no—
354C4×C59—41no—
355C4×C59—41no—
356C4×C59—81no—
357C4×C59C2×C4×D411yescharacteristic
358C4×C59#52011yescharacteristic
359C4×C59#54711yescharacteristic
360C4×C59#55311yescharacteristic
361Dic59—42no—
362Dic59—81no—
363Dic59—81no—
364C2×#459—591no—
365C2×#442—591no—
366C2×C4×D8—591no—
367#2366D5911yescharacteristic, complemented
368#2349—591no—
369#1961—591no—
370#1949—591no—
371#1936—591no—
372#1934—591no—
373#1879—591no—
374#1879—591no—
375#1864—591no—
376#1862—591no—
377#1771—591no—
378#1762—591no—
379C2×C59—82no—
380C2×C59—82no—
381C2×C59#236111yescharacteristic
382C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C59#294811yescharacteristic
384C2×C59#326411yescharacteristic
385C2×C59#326811yescharacteristic
386C2×C59#336611yescharacteristic
387C2×C59#337011yescharacteristic
388D59—44no—
389C22×D8—591no—
390C22×D8—591no—
391C2×#127C2×D5911yescharacteristic
392C2×C4×D4—21no—
393C2×C4×D4—591no—
394C2×C4×D4—591no—
395C2×C4×D4—591no—
396C2×C4×D4C2×D5911yescharacteristic
397C2×C4×D4C2×D5911yescharacteristic
398#459—598no—
399#442—1184no—
400C4×D8—1184no—
401C2×#107—591no—
402C2×#106—591no—
403C2×C4⋊C8—591no—
404C2×#102—591no—
405C2×#102—591no—
406C2×#102—591no—
407C2×#102—591no—
408C2×#102—591no—
409C2×#102—591no—
410C2×#102—591no—
411C2×#102—591no—
412C2×#97—591no—
413C2×#97—591no—
414C2×C4×C8—591no—
415#390—21no—
416#390C2×D5911yescharacteristic
417#390C2×D5911yescharacteristic
418#389—591no—
419#389—591no—
420#386—21no—
421#386—21no—
422#385—1181no—
423#385—1181no—
424#382—591no—
425#380—1181no—
426C4×C4⋊C4C2×D5911yescharacteristic
427C4×C4⋊C4C2×D5911yescharacteristic
428C2×#95—1181no—
429#340—591no—
430#340—591no—
431#340—591no—
432#340—591no—
433#336—591no—
434#336—591no—
435C59#2300811yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—591no—
439C22×D4C22×D5911yescharacteristic
440C22×D4C22×D5911yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—1181no—
444C23×C4—1181no—
445C23×C4—1181no—
446C2×D8—594no—
447C2×D8—594no—
448C2×D8—1182no—
449C2×D8—1182no—
450C2×D8—1182no—
451C2×D8—1182no—
452C22×C8—591no—
453C22×C8—591no—
454C22×C8—591no—
455C22×C8—591no—
456#127—22no—
457#127C4×D5914yescomplemented
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—41no—
461C4×D4—41no—
462C4×D4—44no—
463C4×D4—594no—
464C4×D4—1182no—
465C4×D4—1182no—
466C4×D4—1182no—
467C4×D4—2361no—
468C4×D4—2361no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4C22⋊D5911yescharacteristic
475C2×C4⋊C4C22⋊D5911yescharacteristic
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4—1181no—
487C2×C42—21no—
488C2×C42C22×D5911yescharacteristic
489C2×C42C22×D5911yescharacteristic
490C2×C42C22×D5911yescharacteristic
491#107—1182no—
492#106—1182no—
493C4⋊C8—594no—
494#102—594no—
495#102—594no—
496#102—594no—
497#102—1182no—
498#102—1182no—
499#102—1182no—
500#102—2361no—
501#102—2361no—
502#97—1182no—
503#97—1182no—
504C4×C8—1182no—
505#95—21no—
506#95—1181no—
507#95—1181no—
508#95—1181no—
509#95—1181no—
510#95C22⋊D5911yescharacteristic
511#95C22⋊D5911yescharacteristic
512C24—21no—
513C24—21no—
514C24—1181no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4—592no—
532C2×D4—592no—
533C2×D4—592no—
534C2×D4—1181no—
535C2×D4—1181no—
536C2×D4—1181no—
537C2×D4C2×C4×D5912yes—
538C2×D4C2×C4×D5912yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—1181no—
548C22×C4—1184no—
549C22×C4—1181no—
550C22×C4—1181no—
551C22×C4—4721no—
552C22×C4—4721no—
553C22×C4—4721no—
554C22×C4—4721no—
555C22×C4—2362no—
556C22×C4—2362no—
557C22×C4—2362no—
558C22×C4—2362no—
559C22×C4C2×C22⋊D5911yescharacteristic
560C22×C4C2×C22⋊D5911yescharacteristic
561C22×C4C2×C22⋊D5911yescharacteristic
562C22×C4C2×C22⋊D5911yescharacteristic
563C22×C4C2×C22⋊D5911yescharacteristic
564C22×C4C2×C22⋊D5911yescharacteristic
565C22×C4C23×D5911yescharacteristic
566D8—1188no—
567D8—1188no—
568C2×C8—592no—
569C2×C8—592no—
570C2×C8—592no—
571C2×C8—1181no—
572C2×C8—1181no—
573C2×C8—1181no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8—1181no—
579C2×C8—1181no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—41no—
585C4⋊C4—592no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—4721no—
592C4⋊C4—4721no—
593C4⋊C4D4×D5912yes—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—1184no—
601C22⋊C4—2362no—
602C22⋊C4—2362no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42C2×C4×D5912yes—
609C42#1174568512yes—
610C23—22no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—1182no—
625C23—1182no—
626C23—1182no—
627C23—2361no—
628C23—2361no—
629C23—2361no—
630C23—2361no—
631C23C22×C22⋊D5911yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—84no—
642D4—594no—
643D4—1182no—
644D4—1182no—
645D4—1182no—
646C2×C4—21no—
647C2×C4—21no—
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—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—1182no—
670C2×C4—4724no—
671C2×C4—4724no—
672C2×C4—4724no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4C4×C22⋊D5912yes—
682C2×C4C4×C22⋊D5912yes—
683C2×C4#1427375312yes—
684C2×C4C22×C4×D5911yescharacteristic
685C2×C4C2×D4×D5911yescharacteristic
686C2×C4#41×D5911yescharacteristic
687C2×C4C2×#1174568511yescharacteristic
688C2×C4#1427377211yescharacteristic
689C2×C4#1427377411yescharacteristic
690C8—1182no—
691C8—1182no—
692C8—1182no—
693C8—2361no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—1184no—
709C22—2362no—
710C22—2362no—
711C22—2362no—
712C22—2362no—
713C22—2362no—
714C22—2362no—
715C22C2×C4×C22⋊D5911yescharacteristic
716C22D4×C22⋊D5911yescharacteristic
717C22#1683805911yescharacteristic
718C22C2×#1427375311yescharacteristic
719C22#1683820011yescharacteristic
720C22#1683820511yescharacteristic
721C22#1683820511yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—4721no—
731C4—4721no—
732C4—2362no—
733C4C4×D4×D5911yescharacteristic
734C4#1683788111yescharacteristic
735C4#1683805711yescharacteristic
736C4#1683810211yescharacteristic
737C2—82no—
738C2—82no—
739C2—2364no—
740C2#2142710811yescharacteristic
741C2C4×#1427375311yescharacteristic
742C2#2143294611yescharacteristic
743C2#2143557211yescharacteristic
744C2#2143563711yescharacteristic
745C2#2143679911yescharacteristic
746C2#2143684311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2366C2
socleC23×C59C22×D4
prime radicalC2×#16837594C2
cosocleC22×C4×C59C24
hypercenter#2366D59
hypocenterC59#23008
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
2. C2×#16837512C2semidirect
3. C2×C4×#11745669C2semidirect
4. #21427007C2semidirect
5. #21424921C2semidirect
6. #21424864C2semidirect
7. #21424796C2semidirect
8. #21424782C2semidirect
9. #21424447C2semidirect
10. #21424447C2semidirect
11. #21424357C2semidirect
12. #21424343C2semidirect
13. #21423971C2semidirect
14. #21423924C2semidirect
15. C59×#2366C2semidirect
21. #16837594C4semidirect
70. C2×#11745669C2×C4semidirect
71. C2×#11745669C2×C4semidirect
81. C4×D236C2×C4semidirect
92. C4⋊(C59⋊C8)C2×C4semidirect
97. #14273648C2×C4semidirect
98. #14273648C2×C4semidirect
100. #14273647D4semidirect
115. #127×C59C2×C4semidirect
312. D236C4×D4semidirect
367. #2366D59semidirect
435. C59#23008semidirect
457. #127C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375942
C2×#168375122
C2×C4×#117456692
#214270072
#214249212
#214248642
#214247962
#214247822
#214244472
#214243572
#214243432
#214239712
#214239242
C59×#23662
#2300859