Finite Group Databasebeta

← #28594513

Subgroups — #28594513

Order 15104.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837564C211yesmaximal, characteristic
2C2×#16837502C211yesmaximal, characteristic, complemented
3C2×C4×#11745672C211yesmaximal, characteristic, complemented
4#21426778C211yesmaximal, characteristic, complemented
5#21424437C211yesmaximal, characteristic, complemented
6#21424430C211yesmaximal, characteristic, complemented
7#21424403C211yesmaximal, characteristic, complemented
8#21424350C211yesmaximal, characteristic, complemented
9#21424343C211yesmaximal, characteristic, complemented
10#21424284C211yesmaximal, characteristic, complemented
11#21424036C211yesmaximal, characteristic
12#21423926C211yesmaximal, characteristic, complemented
13C4×#14273648C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic, complemented
15C2×C59×#520C211yesmaximal, characteristic
16C22×#11745672C2211yescharacteristic
17C22×#11745670C2211yescharacteristic
18C2×#14273706C2211yescharacteristic
19C2×C4×Dic118C2211yescharacteristic
20#16837564C418yescomplemented
21#16837502—24no—
22C4×#11745672—24no—
23C2×#14273660C2211yescharacteristic
24C2×#14273660C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273650C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×#14273638C2211yescharacteristic
36C2×C4×C59⋊C8C2211yescharacteristic
37#16837308C2211yescharacteristic
38#16837300C2211yescharacteristic
39#16837297—21no—
40#16837296—21no—
41#16837290—21no—
42#16837283—21no—
43#16837262C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C22×#41×C59C2211yescharacteristic
52C59×#520—24no—
53C59×#520—24no—
54C2×C4×Q8×C59C2211yescharacteristic
55C2×C4×Q8×C59C2211yescharacteristic
56C2×C4×D4×C59—21no—
57C2×C4×D4×C59—21no—
58C2×C4×D4×C59C2211yescharacteristic
59C2×C4×D4×C59C2211yescharacteristic
60C2×#117×C59—21no—
61C2×#117×C59C2211yescharacteristic
62C22×C4⋊C4×C59—21no—
63C22×C4⋊C4×C59C2211yescharacteristic
64C22×Dic118C2311yescharacteristic
65C2×#11745672—22no—
66C2×#11745672—22no—
67C2×#11745672C2×C414yescomplemented
68C2×#11745670—22no—
69C2×#11745670—22no—
70C2×#11745670C2×C414yescomplemented
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273706—22no—
76#14273706C2×C414yescomplemented
77C4×Dic118—22no—
78C4×Dic118—22no—
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×Dic59⋊C4—21no—
83C2×Dic59⋊C4—21no—
84C2×Dic59⋊C4—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C4×Dic59—21no—
88C2×C4×Dic59—21no—
89#14273660—22no—
90#14273660—22no—
91#14273651—22no—
92#14273651—22no—
93#14273651C2×C414yescomplemented
94#14273650—22no—
95#14273650—22no—
96#14273648—22no—
97#14273648—22no—
98#14273648C2×C414yescomplemented
99C22⋊(C59⋊C8)—22no—
100C22⋊(C59⋊C8)C2×C414yescomplemented
101#14273638—22no—
102C4×C59⋊C8—22no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C2×#41×C59—22no—
109C2×#41×C59—22no—
110C2×#41×C59—22no—
111C2×#41×C59—22no—
112C2×#41×C59—22no—
113C2×#41×C59C2×C414yes—
114C22×Q8×C59C2311yescharacteristic
115C22×D4×C59—21no—
116C22×D4×C59C2311yescharacteristic
117C23×C4×C59—21no—
118C23×C4×C59—21no—
119C23×C4×C59—21no—
120C23×C4×C59—21no—
121C23×C4×C59C2311yescharacteristic
122C4×Q8×C59—22no—
123C4×Q8×C59—22no—
124C4×Q8×C59—22no—
125C4×Q8×C59D414yes—
126C4×D4×C59—28no—
127C4×D4×C59—28no—
128C4×D4×C59—22no—
129C4×D4×C59—22no—
130C4×D4×C59—22no—
131C4×D4×C59D414yes—
132#117×C59—28no—
133#117×C59—22no—
134#117×C59—22no—
135C2×C4⋊C4×C59—28no—
136C2×C4⋊C4×C59—21no—
137C2×C4⋊C4×C59—21no—
138C2×C4⋊C4×C59—21no—
139C2×C4⋊C4×C59—22no—
140C2×C4⋊C4×C59—22no—
141C2×C4⋊C4×C59D411yescharacteristic
142C2×C4⋊C4×C59D411yescharacteristic
143C2×C4⋊C4×C59C2311yescharacteristic
144C2×C4⋊C4×C59C2311yescharacteristic
145C2×C22⋊C4×C59—21no—
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59D411yescharacteristic
148C2×C22⋊C4×C59D411yescharacteristic
149C2×C42×C59—21no—
150C2×C42×C59—21no—
151C2×C42×C59C2311yescharacteristic
152C2×C42×C59C2311yescharacteristic
153C24×C59—21no—
154C24×C59C2×D411yescharacteristic
155#41×C59—28no—
156#41×C59—28no—
157#41×C59—28no—
158#41×C59—28no—
159C2×Q8×C59—21no—
160C2×Q8×C59—21no—
161C2×Q8×C59—21no—
162C2×Q8×C59C22×C412yes—
163C2×Q8×C59C2×D412yes—
164C2×Q8×C59#4112yes—
165C2×D4×C59—24no—
166C2×D4×C59—24no—
167C2×D4×C59—24no—
168C2×D4×C59—21no—
169C2×D4×C59—21no—
170C2×D4×C59—21no—
171C2×D4×C59C22×C412yes—
172C2×D4×C59C2×D412yes—
173C2×D4×C59#4112yes—
174C22×C4×C59—24no—
175C22×C4×C59—24no—
176C22×C4×C59—21no—
177C22×C4×C59—24no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—24no—
185C22×C4×C59—24no—
186C22×C4×C59—24no—
187C22×C4×C59—81no—
188C22×C4×C59—81no—
189C22×C4×C59—81no—
190C22×C4×C59—81no—
191C22×C4×C59—81no—
192C22×C4×C59—81no—
193C22×C4×C59C22×C412yes—
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59#4112yes—
200C22×C4×C59C2411yescharacteristic
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C2×Dic118—21no—
206C2×Dic118—21no—
207C2×Dic118—21no—
208C2×Dic118—21no—
209C2×Dic118—21no—
210C2×Dic118C22×C412yes—
211C4⋊C4×C59—24no—
212C4⋊C4×C59—24no—
213C4⋊C4×C59—22no—
214C4⋊C4×C59—24no—
215C4⋊C4×C59—22no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59C2×D412yes—
219C4⋊C4×C59C2×D412yes—
220C22⋊C4×C59—24no—
221C22⋊C4×C59—24no—
222C22⋊C4×C59—22no—
223C22⋊C4×C59—22no—
224C42×C59—24no—
225C42×C59—24no—
226C42×C59—21no—
227C42×C59—21no—
228C42×C59C2×D412yes—
229C42×C59C2×D412yes—
230C22⋊Dic59—24no—
231C22⋊Dic59—81no—
232#11745672—28no—
233#11745670—28no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59C22×C412yes—
240Dic59⋊C4—24no—
241Dic59⋊C4—42no—
242Dic59⋊C4—81no—
243C4×Dic59—42no—
244C4×Dic59—81no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8—21no—
255C2×C59⋊C8C22×C412yes—
256C2×C59⋊C8C22×C412yes—
257C23×C59—22no—
258C23×C59—21no—
259C23×C59—22no—
260C23×C59—21no—
261C23×C59—22no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—21no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59C4×D412yes—
271C23×C59C22×D411yescharacteristic
272Q8×C59—22no—
273Q8×C59—22no—
274Q8×C59—22no—
275Q8×C59C4×D414yes—
276D4×C59—216no—
277D4×C59—22no—
278D4×C59—22no—
279D4×C59—22no—
280D4×C59C4×D414yes—
281C2×C4×C59—216no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—22no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—21no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—84no—
308C2×C4×C59—84no—
309C2×C4×C59—84no—
310C2×C4×C59C4×D412yes—
311C2×C4×C59#12012yes—
312C2×C4×C59#12012yes—
313C2×C4×C59C23×C411yescharacteristic
314C2×C4×C59C22×D411yescharacteristic
315C2×C4×C59C22×D411yescharacteristic
316C2×C4×C59C2×#4111yescharacteristic
317C2×C4×C59C2×#4111yescharacteristic
318C2×C4×C59C2×#4111yescharacteristic
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—41no—
328C2×Dic59—41no—
329C2×Dic59—41no—
330C2×Dic59—41no—
331Dic118—22no—
332Dic118—22no—
333Dic118—41no—
334Dic118—41no—
335C59⋊C8—22no—
336C59⋊C8—22no—
337C59⋊C8—41no—
338C59⋊C8—41no—
339#21465—591nomaximal, Sylow
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—24no—
344C22×C59—41no—
345C22×C59—42no—
346C22×C59—41no—
347C22×C59—42no—
348C22×C59—42no—
349C22×C59—42no—
350C22×C59—41no—
351C22×C59—42no—
352C22×C59—41no—
353C22×C59—42no—
354C22×C59C2×C4×D411yescharacteristic
355C22×C59C2×#12011yescharacteristic
356C22×C59#52511yescharacteristic
357C22×C59#57611yescharacteristic
358C22×C59#57711yescharacteristic
359C22×C59#57811yescharacteristic
360C22×C59#57811yescharacteristic
361C4×C59—22no—
362C4×C59—22no—
363C4×C59—22no—
364C4×C59—24no—
365C4×C59—41no—
366C4×C59—41no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59C2×C4×D411yescharacteristic
370C4×C59C2×C4×D411yescharacteristic
371C4×C59#52511yescharacteristic
372C4×C59#52511yescharacteristic
373Dic59—42no—
374Dic59—42no—
375Dic59—81no—
376Dic59—81no—
377C2×#520D5911yescharacteristic
378C2×#452—591no—
379C2×#440—591no—
380C2×C4×Q16—591no—
381#2323—591no—
382#1878—591no—
383#1877—591no—
384#1872—591no—
385#1863—591no—
386#1862—591no—
387#1852—591no—
388#1788—591no—
389#1763—591no—
390C4×#102—591no—
391#1750—591no—
392C2×C59—42no—
393C2×C59—44no—
394C2×C59C4×#12011yescharacteristic
395C2×C59#294711yescharacteristic
396C2×C59#295111yescharacteristic
397C2×C59#301111yescharacteristic
398C2×C59#301211yescharacteristic
399C2×C59#312011yescharacteristic
400C2×C59#312411yescharacteristic
401C22×#41C2×D5911yescharacteristic
402C22×Q16—591no—
403C22×SD16—591no—
404C2×C22⋊Q8—591no—
405#520—24no—
406#520—24no—
407C2×C4×Q8—591no—
408C2×C4×Q8C2×D5911yescharacteristic
409C2×C4×Q8C2×D5911yescharacteristic
410C2×C4×D4—21no—
411C2×C4×D4—21no—
412C2×C4×D4C2×D5911yescharacteristic
413C2×C4×D4C2×D5911yescharacteristic
414C2×#117—21no—
415C2×#117C2×D5911yescharacteristic
416C22×C4⋊C4—21no—
417C22×C4⋊C4C2×D5911yescharacteristic
418#452—598no—
419#440—1184no—
420C4×Q16—1184no—
421C2×#107—591no—
422C2×#107—591no—
423C2×#103—591no—
424C2×#103—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#102—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×C22⋊C8—591no—
432C2×C22⋊C8—591no—
433C2×#97—591no—
434C2×C4×C8—591no—
435#391—591no—
436#389—591no—
437#389—1181no—
438#388—1181no—
439#388—1181no—
440#387—1181no—
441#380—591no—
442C4×C4⋊C4—591no—
443#340—591no—
444#340—591no—
445#340—591no—
446#340—591no—
447#336—591no—
448#336—591no—
449C59#2146511yescharacteristic, complemented, Sylow
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C4×D5914yes—
456C22×Q8—591no—
457C22×Q8C22×D5911yescharacteristic
458C22×D4—21no—
459C22×D4C22×D5911yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C22×D5911yescharacteristic
465C2×Q16—594no—
466C2×Q16—1182no—
467C2×Q16—1182no—
468C2×SD16—594no—
469C2×SD16—1182no—
470C2×SD16—1182no—
471C22×C8—591no—
472C22×C8—591no—
473C22×C8—591no—
474C22×C8—591no—
475C22⋊Q8—594no—
476C22⋊Q8—1182no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—1182no—
481C4×Q8—1182no—
482C4×Q8C22⋊D5914yes—
483C4×D4—28no—
484C4×D4—28no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4C22⋊D5914yes—
489#117—28no—
490#117—22no—
491#117—22no—
492C2×C4⋊C4—28no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4C22⋊D5911yescharacteristic
505C2×C4⋊C4C22⋊D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C4⋊C4C22×D5911yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4C22⋊D5911yescharacteristic
513C2×C22⋊C4C22⋊D5911yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—1181no—
517C2×C42—1181no—
518C2×C42C22×D5911yescharacteristic
519C2×C42C22×D5911yescharacteristic
520#107—1182no—
521#107—1182no—
522#103—594no—
523#103—1182no—
524#103—1182no—
525#103—1182no—
526#103—1182no—
527#102—594no—
528#102—1182no—
529#102—1182no—
530C22⋊C8—594no—
531C22⋊C8—1182no—
532#97—1182no—
533C4×C8—1182no—
534#95—1181no—
535#95—1181no—
536#95—1181no—
537#95—1181no—
538#95—1181no—
539C24—21no—
540C24C2×C22⋊D5911yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—592no—
549C2×Q8—1181no—
550C2×Q8—1181no—
551C2×Q8—1181no—
552C2×Q8—1181no—
553C2×Q8—1181no—
554C2×Q8C2×C4×D5912yes—
555C2×Q8#1174568512yes—
556C2×Q8C2×C22⋊D5912yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C2×C4×D5912yes—
564C2×D4#1174568512yes—
565C2×D4C2×C22⋊D5912yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—1181no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4C2×C4×D5912yes—
590C22×C4#1174568512yes—
591C22×C4C2×C22⋊D5911yescharacteristic
592C22×C4C2×C22⋊D5911yescharacteristic
593C22×C4C2×C22⋊D5911yescharacteristic
594C22×C4C2×C22⋊D5911yescharacteristic
595C22×C4C2×C22⋊D5911yescharacteristic
596C22×C4C23×D5911yescharacteristic
597Q16—1188no—
598SD16—1188no—
599C2×C8—592no—
600C2×C8—592no—
601C2×C8—1181no—
602C2×C8—1181no—
603C2×C8—1181no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—592no—
619C4⋊C4—1184no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—1181no—
624C4⋊C4—1181no—
625C4⋊C4—4721no—
626C4⋊C4—2362no—
627C4⋊C4C2×C22⋊D5912yes—
628C4⋊C4C2×C22⋊D5912yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—1184no—
634C22⋊C4—4721no—
635C42—24no—
636C42—24no—
637C42—21no—
638C42—21no—
639C42—4721no—
640C42—2362no—
641C42C2×C22⋊D5912yes—
642C42C2×C22⋊D5912yes—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—22no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C4×C22⋊D5912yes—
657C23C22×C22⋊D5911yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—1182no—
662Q8—1182no—
663Q8—2361no—
664Q8—2361no—
665Q8C4×C22⋊D5914yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4C4×C22⋊D5914yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—84no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—2361no—
703C2×C4—2361no—
704C2×C4—2361no—
705C2×C4—2361no—
706C2×C4—2361no—
707C2×C4—2361no—
708C2×C4—2361no—
709C2×C4—2361no—
710C2×C4—2361no—
711C2×C4—2361no—
712C2×C4C4×C22⋊D5912yes—
713C2×C4#1427369612yes—
714C2×C4#1427369612yes—
715C2×C4C22×C4×D5911yescharacteristic
716C2×C4C22×C22⋊D5911yescharacteristic
717C2×C4C22×C22⋊D5911yescharacteristic
718C2×C4C2×#1174568511yescharacteristic
719C2×C4C2×#1174568511yescharacteristic
720C2×C4C2×#1174568511yescharacteristic
721C8—1182no—
722C8—1182no—
723C8—2361no—
724C8—2361no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×C4×C22⋊D5911yescharacteristic
740C22C2×#1427369611yescharacteristic
741C22#1683791311yescharacteristic
742C22#1683820511yescharacteristic
743C22#1683821311yescharacteristic
744C22#1683821711yescharacteristic
745C22#1683821711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—24no—
750C4—41no—
751C4—41no—
752C4—42no—
753C4—42no—
754C4—4721no—
755C4—4721no—
756C4—2362no—
757C4—2362no—
758C4C2×C4×C22⋊D5911yescharacteristic
759C4C2×C4×C22⋊D5911yescharacteristic
760C4#1683791311yescharacteristic
761C4#1683791311yescharacteristic
762C2—42no—
763C2—44no—
764C2C4×#1427369611yescharacteristic
765C2#2143293511yescharacteristic
766C2#2143296911yescharacteristic
767C2#2143339111yescharacteristic
768C2#2143340011yescharacteristic
769C2#2143431011yescharacteristic
770C2#2143435811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#520C2
socleC23×C59C22×D4
prime radicalC22×#41×C59C22
cosocleC22×C4×C59C24
hypercenterC2×#520D59
hypocenterC59#21465
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#16837502C2semidirect
3. C2×C4×#11745672C2semidirect
4. #21426778C2semidirect
5. #21424437C2semidirect
6. #21424430C2semidirect
7. #21424403C2semidirect
8. #21424350C2semidirect
9. #21424343C2semidirect
10. #21424284C2semidirect
12. #21423926C2semidirect
13. C4×#14273648C2semidirect
14. #21423862C2semidirect
20. #16837564C4semidirect
67. C2×#11745672C2×C4semidirect
70. C2×#11745670C2×C4semidirect
76. #14273706C2×C4semidirect
93. #14273651C2×C4semidirect
98. #14273648C2×C4semidirect
100. C22⋊(C59⋊C8)C2×C4semidirect
449. C59#21465semidirect

Maximal subgroups

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

subgroupindex
C2×#168375642
C2×#168375022
C2×C4×#117456722
#214267782
#214244372
#214244302
#214244032
#214243502
#214243432
#214242842
#214240362
#214239262
C4×#142736482
#214238622
C2×C59×#5202
#2146559