Finite Group Databasebeta

← #28556338

Subgroups — #28556338

Order 15104.

1298 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437776C211yesmaximal, characteristic
2#21432545C211yesmaximal, characteristic, complemented
3#21422667C211yesmaximal, characteristic, complemented
4#21422650C212yesmaximal, complemented
5#21422637C211yesmaximal, characteristic, complemented
6#21422628C212yesmaximal, complemented
7#21422615C211yesmaximal, characteristic, complemented
8#21422598C212yesmaximal, complemented
9#21422585C211yesmaximal, characteristic, complemented
10C2×#16837138C212yesmaximal, complemented
11C59×#2339C211yesmaximal, characteristic, complemented
12C2×#14273774C411yescharacteristic, complemented
13C2×#14273734—21no—
14Q8×C22⋊D59—21no—
15#16838059—21no—
16#16838051—21no—
17#16838051—22no—
18#16838046—21no—
19#16838046—22no—
20#16837980C411yescharacteristic, complemented
21#16837980C412yescomplemented
22#16837973C411yescharacteristic, complemented
23#16837973C412yescomplemented
24#16837913C2212yes—
25#16837913C2211yescharacteristic
26C2×#14273706C2211yescharacteristic
27C2×#14273706C2212yes—
28#16837885C411yescharacteristic, complemented
29#16837369—22no—
30#16837369—21no—
31#16837366C2212yes—
32#16837366C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2212yes—
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35#16837138C2212yes—
36#16837138C2212yes—
37#16837138C2212yes—
38#16837138C2211yescharacteristic
39#16837138C2212yes—
40#16837138C2212yes—
41#16837138C2211yescharacteristic
42#16837135C2211yescharacteristic
43#16837135C2212yes—
44#16837135C2211yescharacteristic
45C22×#41×C59C2211yescharacteristic
46C2×C4×D4×C59—21no—
47C59×#391—21no—
48C59×#386—22no—
49C59×#381C2212yes—
50C59×#380C2211yescharacteristic
51C4×C22⋊C4×C59C2211yescharacteristic
52C2×#95×C59C2212yes—
53#14273774—44no—
54C2×#11745685C2×C412yescomplemented
55C2×#11745685C2×C411yescharacteristic, complemented
56C2×#11745687—22no—
57C2×#11745687—21no—
58C22×Dic118C2×C412yescomplemented
59C22×Dic118C2×C411yescharacteristic, complemented
60C2×Q8×D59—21no—
61#14273734—44no—
62C2×#11745664—22no—
63C2×#11745664—21no—
64C22×C59⋊C8—22no—
65C22×C59⋊C8—21no—
66#14273725—21no—
67#14273725—22no—
68#14273714—21no—
69#14273714—22no—
70#14273710—22no—
71#14273710—21no—
72#14273708—22no—
73#14273708—22no—
74#14273708—22no—
75#14273706—21no—
76#14273706—22no—
77#14273706—21no—
78#14273706—22no—
79#14273706C2×C412yescomplemented
80#14273706C2×C412yescomplemented
81#14273706C2×C412yescomplemented
82#14273706C2×C412yescomplemented
83#14273706C2×C411yescharacteristic, complemented
84#14273706C2312yes—
85#14273706C2311yescharacteristic
86#14273703—21no—
87#14273703—22no—
88#14273701C2×C412yescomplemented
89#14273701C2×C411yescharacteristic, complemented
90#14273701C2311yescharacteristic
91#14273699—22no—
92#14273699—22no—
93#14273699—22no—
94#14273698—21no—
95#14273698—22no—
96#14273696—22no—
97#14273696—21no—
98Q8×Dic59—21no—
99D4×Dic59—22no—
100D4×Dic59—21no—
101C4×C22⋊D59—21no—
102C4×C22⋊D59—22no—
103C4×C22⋊D59—21no—
104C4×C22⋊D59—22no—
105#14273686C2×C412yescomplemented
106#14273686C2×C411yescharacteristic, complemented
107C2×C4⋊Dic59C2×C411yescharacteristic, complemented
108C2×C4⋊Dic59C2×C412yescomplemented
109C2×Dic59⋊C4—22no—
110C2×Dic59⋊C4—21no—
111C2×C22⋊Dic59—22no—
112C2×C22⋊Dic59—21no—
113C22⋊(C59⋊C8)—21no—
114C22⋊(C59⋊C8)—22no—
115C22⋊(C59⋊C8)—21no—
116C22⋊(C59⋊C8)—22no—
117C22⋊(C59⋊C8)C2311yescharacteristic
118C22⋊(C59⋊C8)C2311yescharacteristic
119C22⋊(C59⋊C8)C2312yes—
120C2×#41×C59—44no—
121C2×#41×C59C2×C411yescharacteristic
122C2×#41×C59C2×C411yescharacteristic
123C2×#41×C59C2×C412yes—
124C2×#41×C59D411yescharacteristic
125C2×#41×C59D412yes—
126C2×#41×C59D411yescharacteristic
127C22×Q8×C59D411yescharacteristic
128C22×D4×C59D411yescharacteristic
129C22×D4×C59D412yes—
130C23×C4×C59—22no—
131C23×C4×C59C2312yes—
132C23×C4×C59C2311yescharacteristic
133C4×D4×C59—44no—
134C2×C4⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—22no—
137C2×C22⋊C4×C59—21no—
138C2×C42×C59—21no—
139#95×C59—22no—
140#95×C59—22no—
141#95×C59C2311yescharacteristic
142#95×C59C2312yes—
143#95×C59C2311yescharacteristic
144C24×C59C2×D412yes—
145C24×C59C2×D411yescharacteristic
146#41×C59—24no—
147#41×C59—24no—
148#41×C59—44no—
149#41×C59—44no—
150#41×C59—42no—
151#41×C59—42no—
152C2×Q8×C59—42no—
153C2×Q8×C59C22⋊C411yescharacteristic
154C2×Q8×C59C22⋊C411yescharacteristic
155C2×Q8×C59C22⋊C412yes—
156C2×D4×C59—24no—
157C2×D4×C59—44no—
158C2×D4×C59C22⋊C412yes—
159C2×D4×C59C22⋊C411yescharacteristic
160C2×D4×C59C22⋊C412yes—
161C2×D4×C59C22⋊C412yes—
162C2×D4×C59C22⋊C412yes—
163C2×D4×C59C22⋊C412yes—
164C2×D4×C59C22⋊C411yescharacteristic
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—22no—
168C22×C4×C59—42no—
169C22×C4×C59—44no—
170C22×C4×C59—44no—
171C22×C4×C59—44no—
172C22×C4×C59—82no—
173C22×C4×C59C22×C412yes—
174C22×C4×C59C22×C411yescharacteristic
175C22×C4×C59C22×C412yes—
176C22×C4×C59C22×C411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D412yes—
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D412yes—
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D412yes—
183C22×C4×C59C2411yescharacteristic
184C2×C22⋊D59—21no—
185C2×C22⋊D59—22no—
186C2×C22⋊D59—21no—
187C2×C22⋊D59—21no—
188C2×C22⋊D59—22no—
189C22×Dic59—21no—
190C22×Dic59—22no—
191C22×Dic59—21no—
192C22×Dic59—22no—
193Q8×D59—44no—
194#11745687—48no—
195#11745687—44no—
196#11745685—44no—
197#11745685—42no—
198C2×D236C22×C411yescharacteristic
199C2×C4×D59—22no—
200C2×C4×D59—21no—
201C2×Dic118—22no—
202C2×Dic118—21no—
203C2×Dic118—44no—
204C2×Dic118—42no—
205C2×Dic118C22×C411yescharacteristic
206C2×Dic118C22×C412yes—
207C4⋊C4×C59—42no—
208C22⋊C4×C59—42no—
209C22⋊C4×C59—44no—
210C22⋊C4×C59—81no—
211C42×C59—42no—
212C22⋊Dic59—22no—
213C22⋊Dic59—22no—
214C22⋊Dic59—22no—
215C22⋊Dic59—21no—
216C22⋊Dic59—22no—
217C22⋊Dic59—21no—
218C22⋊Dic59—22no—
219C22⋊Dic59—21no—
220C22⋊Dic59—22no—
221(C2×D59)⋊C4—21no—
222(C2×D59)⋊C4—22no—
223(C2×D59)⋊C4—21no—
224C4⋊Dic59—22no—
225C4⋊Dic59—21no—
226C4⋊Dic59C22×C412yes—
227C4⋊Dic59C22×C411yescharacteristic
228C4⋊Dic59C22×C411yescharacteristic
229Dic59⋊C4—22no—
230Dic59⋊C4—22no—
231Dic59⋊C4—22no—
232Dic59⋊C4—21no—
233Dic59⋊C4—22no—
234Dic59⋊C4—21no—
235Dic59⋊C4—22no—
236C4×Dic59—22no—
237C4×Dic59—21no—
238#11745664—44no—
239#11745664—42no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—22no—
243C2×C59⋊C8—44no—
244C2×C59⋊C8—42no—
245C23×C59—22no—
246C23×C59—22no—
247C23×C59—24no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—42no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59C2×C22⋊C411yescharacteristic
254C23×C59C2×C22⋊C412yes—
255C23×C59C2×C22⋊C411yescharacteristic
256C23×C59C2×C22⋊C412yes—
257C23×C59C22×D411yescharacteristic
258C22×D59—21no—
259Q8×C59—22no—
260Q8×C59—22no—
261Q8×C59—42no—
262D4×C59—24no—
263D4×C59—24no—
264D4×C59—24no—
265D4×C59—22no—
266D4×C59—42no—
267D4×C59—42no—
268D4×C59#9914yes—
269C2×C4×C59—24no—
270C2×C4×C59—24no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59—42no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—42no—
285C2×C4×C59—41no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59—41no—
289C2×C4×C59—88no—
290C2×C4×C59C2×C22⋊C412yes—
291C2×C4×C59C2×C22⋊C411yescharacteristic
292C2×C4×C59C2×C22⋊C412yes—
293C2×C4×C59C2×C22⋊C411yescharacteristic
294C2×C4×C59C23×C411yescharacteristic
295C2×C4×C59C22×D411yescharacteristic
296C22⋊D59—42no—
297C22⋊D59—41no—
298C22⋊D59—41no—
299C22⋊D59—44no—
300C22⋊D59—82no—
301C22⋊D59—81no—
302C2×Dic59—21no—
303C2×Dic59—22no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—22no—
307C2×Dic59—42no—
308C2×Dic59—44no—
309C2×Dic59—82no—
310C2×Dic59—81no—
311D236—41no—
312C4×D59—44no—
313C4×D59—42no—
314Dic118—44no—
315Dic118—42no—
316Dic118—41no—
317Dic118—42no—
318C59⋊C8—41no—
319C59⋊C8—42no—
320C59⋊C8—41no—
321#17608—591nomaximal, Sylow
322C22×C59—21no—
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—21no—
326C22×C59—21no—
327C22×C59—21no—
328C22×C59—22no—
329C22×C59—22no—
330C22×C59—21no—
331C22×C59—21no—
332C22×C59—21no—
333C22×C59—22no—
334C22×C59—21no—
335C22×C59—44no—
336C22×C59—44no—
337C22×C59—81no—
338C22×C59—81no—
339C22×C59C2×#9914yes—
340C22×C59C22×C22⋊C411yescharacteristic
341C22×C59#57711yescharacteristic
342C22×C59#57811yescharacteristic
343C2×D59—41no—
344C2×D59—41no—
345C2×D59—41no—
346C4×C59—21no—
347C4×C59—21no—
348C4×C59—22no—
349C4×C59—21no—
350C4×C59—22no—
351C4×C59—42no—
352C4×C59—81no—
353C4×C59—82no—
354C4×C59C2×#9912yes—
355Dic59—41no—
356Dic59—42no—
357Dic59—41no—
358Dic59—41no—
359Dic59—42no—
360#3489—591no—
361#2880—591no—
362#2339D5911yescharacteristic, complemented
363#1520—591no—
364#1516—592no—
365#1513—591no—
366#1511—592no—
367#1508—591no—
368#1504—592no—
369#1501—591no—
370C2×#328—592no—
371C2×C59—21no—
372C2×C59—21no—
373C2×C59—24no—
374C2×C59—42no—
375C2×C59—41no—
376C2×C59—41no—
377C2×C59C22×#9911yescharacteristic
378C2×C59#289811yescharacteristic
379C2×C59#290111yescharacteristic
380D59—81no—
381C2×2−1+4—591no—
382C22×#41C2×D5911yescharacteristic
383C2×#131—1181no—
384D4×Q8—1181no—
385#548—1181no—
386#547—1181no—
387#547—1182no—
388#546—1181no—
389#546—1182no—
390#537—592no—
391#537—591no—
392#536—591no—
393#536—592no—
394#525—591no—
395#525—592no—
396C2×C22⋊Q8—592no—
397C2×C22⋊Q8—591no—
398#520—591no—
399C2×C4×D4—21no—
400#408—1182no—
401#408—1181no—
402#407—592no—
403#407—591no—
404C2×C22⋊C8—592no—
405C2×C22⋊C8—591no—
406#391—21no—
407#386—22no—
408#381C2×D5912yes—
409#380C2×D5911yescharacteristic
410C4×C22⋊C4C2×D5911yescharacteristic
411C2×#95C2×D5912yes—
412#328—591no—
413#328—592no—
414#328—592no—
415#328—592no—
416#328—591no—
417#328—592no—
418#328—592no—
419#327—591no—
420#327—591no—
421#327—592no—
422C59#1760811yescharacteristic, complemented, Sylow
4232−1+4—2364no—
424C2×#41—44no—
425C2×#41—592no—
426C2×#41—591no—
427C2×#41—1182no—
428C2×#41—1181no—
429C2×#41C4×D5911yescharacteristic
430C2×#41C4×D5912yes—
431C2×#41C4×D5911yescharacteristic
432C2×#41D23611yescharacteristic
433C2×#41D23612yes—
434C2×#41D23611yescharacteristic
435C22×Q8—591no—
436C22×Q8—592no—
437C22×Q8—1181no—
438C22×Q8C22⋊D5911yescharacteristic
439C22×D4C22⋊D5911yescharacteristic
440C22×D4C22⋊D5912yes—
441C23×C4—22no—
442C23×C4C22×D5912yes—
443C23×C4C22×D5911yescharacteristic
444#131—2364no—
445C2×M16—1182no—
446C2×M16—1181no—
447C22×C8—1182no—
448C22×C8—1181no—
449C4⋊Q8—1181no—
450C4⋊Q8—1182no—
451#124—1181no—
452#124—1182no—
453#123—1182no—
454#123—1182no—
455#123—1182no—
456#123—1182no—
457#123—1181no—
458C22⋊Q8—592no—
459C22⋊Q8—592no—
460C22⋊Q8—592no—
461C22⋊Q8—591no—
462C22⋊Q8—592no—
463C22⋊Q8—591no—
464C22⋊Q8—592no—
465C22⋊Q8—1181no—
466C22⋊Q8—1182no—
467C22⋊Q8—1181no—
468C22⋊Q8—1182no—
469C22⋊Q8—1181no—
470C22⋊Q8—1182no—
471#121—591no—
472#121—592no—
473#121—591no—
474#121—1182no—
475#121—1182no—
476#121—1182no—
477#121—1181no—
478#121—1182no—
479#120—1182no—
480#120—1181no—
481C4×Q8—1181no—
482C4×D4—44no—
483C4×D4—1182no—
484C4×D4—1181no—
485C4×D4—1181no—
486C4×D4—1182no—
487C4×D4—1181no—
488C4×D4—1182no—
489#117—591no—
490#117—592no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—592no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—1182no—
495C2×C4⋊C4—1181no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—1182no—
500C2×C22⋊C4—1181no—
501C2×C42—21no—
502C22⋊C8—591no—
503C22⋊C8—591no—
504C22⋊C8—592no—
505C22⋊C8—1181no—
506C22⋊C8—1182no—
507C22⋊C8—1181no—
508C22⋊C8—1182no—
509#95—22no—
510#95—22no—
511#95C22×D5911yescharacteristic
512#95C22×D5912yes—
513#95C22×D5911yescharacteristic
514C24C2×C22⋊D5912yes—
515C24C2×C22⋊D5911yescharacteristic
516#41—24no—
517#41—24no—
518#41—44no—
519#41—44no—
520#41—42no—
521#41—42no—
522#41—2364no—
523#41—2362no—
524#41—2368no—
525#41—2364no—
526C2×Q8—42no—
527C2×Q8—592no—
528C2×Q8—591no—
529C2×Q8—1182no—
530C2×Q8—1181no—
531C2×Q8—2362no—
532C2×Q8—2364no—
533C2×Q8—2364no—
534C2×Q8(C2×D59)⋊C411yescharacteristic
535C2×Q8(C2×D59)⋊C411yescharacteristic
536C2×Q8(C2×D59)⋊C412yes—
537C2×D4—24no—
538C2×D4—44no—
539C2×D4—591no—
540C2×D4—1181no—
541C2×D4—1182no—
542C2×D4—1181no—
543C2×D4—1182no—
544C2×D4—1181no—
545C2×D4(C2×D59)⋊C412yes—
546C2×D4(C2×D59)⋊C412yes—
547C2×D4(C2×D59)⋊C412yes—
548C2×D4(C2×D59)⋊C411yescharacteristic
549C2×D4(C2×D59)⋊C412yes—
550C2×D4(C2×D59)⋊C412yes—
551C2×D4(C2×D59)⋊C411yescharacteristic
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—82no—
560C22×C4—1181no—
561C22×C4—1182no—
562C22×C4—1181no—
563C22×C4—1182no—
564C22×C4—1182no—
565C22×C4—1181no—
566C22×C4C2×C4×D5912yes—
567C22×C4C2×C4×D5911yescharacteristic
568C22×C4C2×C4×D5912yes—
569C22×C4C2×C4×D5911yescharacteristic
570C22×C4C2×D23612yes—
571C22×C4C2×D23611yescharacteristic
572C22×C4C2×D23611yescharacteristic
573C22×C4C2×D23612yes—
574C22×C4C2×C22⋊D5911yescharacteristic
575C22×C4C2×C22⋊D5912yes—
576C22×C4C23×D5911yescharacteristic
577M16—2364no—
578M16—2362no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1182no—
582C2×C8—2364no—
583C2×C8—2362no—
584C4⋊C4—42no—
585C4⋊C4—591no—
586C4⋊C4—592no—
587C4⋊C4—591no—
588C4⋊C4—1182no—
589C4⋊C4—1181no—
590C4⋊C4—1182no—
591C4⋊C4—1182no—
592C4⋊C4—1182no—
593C4⋊C4—1181no—
594C4⋊C4—1182no—
595C4⋊C4—1181no—
596C4⋊C4—1182no—
597C22⋊C4—42no—
598C22⋊C4—44no—
599C22⋊C4—81no—
600C22⋊C4—1182no—
601C22⋊C4—1182no—
602C22⋊C4—1182no—
603C22⋊C4—1181no—
604C22⋊C4—1182no—
605C22⋊C4—1181no—
606C22⋊C4—1182no—
607C22⋊C4—1181no—
608C22⋊C4—1182no—
609C22⋊C4—1181no—
610C22⋊C4—1182no—
611C22⋊C4—1181no—
612C42—42no—
613C42—1182no—
614C42—1181no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—21no—
619C23—21no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—1181no—
624C23C2×(C2×D59)⋊C411yescharacteristic
625C23C2×(C2×D59)⋊C412yes—
626C23C2×(C2×D59)⋊C411yescharacteristic
627C23C2×(C2×D59)⋊C412yes—
628C23C22×C22⋊D5911yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—2362no—
633Q8—2361no—
634Q8—2364no—
635Q8—2362no—
636D4—24no—
637D4—24no—
638D4—24no—
639D4—22no—
640D4—42no—
641D4—42no—
642D4—4722no—
643D4—4721no—
644D4—2361no—
645D4—2362no—
646D4—2361no—
647D4—2361no—
648D4—2364no—
649D4#1427364114yes—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—88no—
671C2×C4—1181no—
672C2×C4—1182no—
673C2×C4—1181no—
674C2×C4—1182no—
675C2×C4—1181no—
676C2×C4—4722no—
677C2×C4—4721no—
678C2×C4—2364no—
679C2×C4—2362no—
680C2×C4—2364no—
681C2×C4—2362no—
682C2×C4C2×(C2×D59)⋊C412yes—
683C2×C4C2×(C2×D59)⋊C411yescharacteristic
684C2×C4C2×(C2×D59)⋊C412yes—
685C2×C4C2×(C2×D59)⋊C411yescharacteristic
686C2×C4C22×C4×D5911yescharacteristic
687C2×C4C22×D23611yescharacteristic
688C8—2361no—
689C8—2362no—
690C8—2361no—
691C22—22no—
692C22—21no—
693C22—22no—
694C22—21no—
695C22—22no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—22no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—81no—
707C22—81no—
708C22—2361no—
709C22—2361no—
710C22—2361no—
711C22C2×#1427364114yes—
712C22C22×(C2×D59)⋊C411yescharacteristic
713C22#1683821311yescharacteristic
714C22#1683821711yescharacteristic
715C4—21no—
716C4—21no—
717C4—22no—
718C4—21no—
719C4—22no—
720C4—42no—
721C4—82no—
722C4—81no—
723C4—2361no—
724C4—2361no—
725C4—2362no—
726C4—2362no—
727C4—2361no—
728C4C2×#1427364112yes—
729C2—21no—
730C2—21no—
731C2—24no—
732C2—42no—
733C2—41no—
734C2—41no—
735C2—4721no—
736C2C22×#1427364111yescharacteristic
737C2#2143262611yescharacteristic
738C2#2143264411yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2339C2
socleC22×C59C22×C22⋊C4
prime radical#21437776C2
cosocleC22×C4×C59C24
hypercenter#2339D59
hypocenterC59#17608
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×#41 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. #21432545C2semidirect
3. #21422667C2semidirect
4. #21422650C2semidirect
5. #21422637C2semidirect
6. #21422628C2semidirect
7. #21422615C2semidirect
8. #21422598C2semidirect
9. #21422585C2semidirect
10. C2×#16837138C2semidirect
11. C59×#2339C2semidirect
12. C2×#14273774C4semidirect
20. #16837980C4semidirect
21. #16837980C4semidirect
22. #16837973C4semidirect
23. #16837973C4semidirect
28. #16837885C4semidirect
54. C2×#11745685C2×C4semidirect
55. C2×#11745685C2×C4semidirect
58. C22×Dic118C2×C4semidirect
59. C22×Dic118C2×C4semidirect
79. #14273706C2×C4semidirect
80. #14273706C2×C4semidirect
81. #14273706C2×C4semidirect
82. #14273706C2×C4semidirect
83. #14273706C2×C4semidirect
88. #14273701C2×C4semidirect
89. #14273701C2×C4semidirect
105. #14273686C2×C4semidirect
106. #14273686C2×C4semidirect
107. C2×C4⋊Dic59C2×C4semidirect
108. C2×C4⋊Dic59C2×C4semidirect
362. #2339D59semidirect
422. C59#17608semidirect

Maximal subgroups

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

subgroupindex
#214377762
#214325452
#214226672
#214226502
#214226372
#214226282
#214226152
#214225982
#214225852
C2×#168371382
C59×#23392
#1760859