Finite Group Databasebeta

← #28632549

Subgroups — #28632549

Order 15104.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837553C211yesmaximal, characteristic
2C2×C4×#11745670C211yesmaximal, characteristic, complemented
3#21427621C211yesmaximal, characteristic, complemented
4#21425629C211yesmaximal, characteristic, complemented
5#21425532C211yesmaximal, characteristic, complemented
6#21425413C211yesmaximal, characteristic, complemented
7#21425292C211yesmaximal, characteristic, complemented
8#21424782C211yesmaximal, characteristic, complemented
9#21424704C211yesmaximal, characteristic, complemented
10#21424454C211yesmaximal, characteristic, complemented
11#21424430C211yesmaximal, characteristic, complemented
12#21424357C211yesmaximal, characteristic, complemented
13#21424096C211yesmaximal, characteristic, complemented
14#21424027C211yesmaximal, characteristic
15D4×C22⋊C4×C59C211yesmaximal, characteristic
16C22×#11745670C2211yescharacteristic
17C22×#11745670C2211yescharacteristic
18C2×#14273706C2211yescharacteristic
19C2×C4×Dic118C2211yescharacteristic, complemented
20#16837553—24no—
21C4×#11745670—24no—
22C2×#14273658C2211yescharacteristic, complemented
23C2×#14273658C2211yescharacteristic, complemented
24C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
25C2×#14273650C2211yescharacteristic, complemented
26C2×#14273650C2211yescharacteristic, complemented
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C4×C59⋊C8C2211yescharacteristic, complemented
36#16837338—21no—
37#16837336—21no—
38#16837308C2211yescharacteristic, complemented
39#16837300C2211yescharacteristic, complemented
40#16837295—21no—
41#16837285—21no—
42#16837272C2211yescharacteristic, complemented
43#16837262C2211yescharacteristic
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837157C2211yescharacteristic, complemented
49#16837157C2211yescharacteristic, complemented
50C23×D4×C59C2211yescharacteristic
51C2×C4×D4×C59C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C22×C22⋊C4×C59—21no—
54C59×#390C2211yescharacteristic
55C59×#390C2211yescharacteristic
56C59×#386—21no—
57C59×#386—21no—
58C59×#380C2211yescharacteristic
59C59×#379—21no—
60C4×C22⋊C4×C59C2211yescharacteristic
61C22×Dic118C2311yescharacteristic
62C2×#11745670—22no—
63C2×#11745670—22no—
64C2×#11745670—22no—
65C2×#11745670—22no—
66C2×#11745670—41no—
67C2×#11745670D414yes—
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72#14273706—22no—
73#14273706—41no—
74C4×Dic118—22no—
75C4×Dic118—41no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×Dic59⋊C4—21no—
82C2×Dic59⋊C4—21no—
83C2×Dic59⋊C4—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C4×Dic59—21no—
87#14273658—22no—
88#14273658—41no—
89C4⋊(C59⋊C8)—41no—
90#14273650—22no—
91#14273650—41no—
92#14273648—22no—
93#14273648—22no—
94#14273648—22no—
95#14273648—22no—
96#14273648—22no—
97#14273648—41no—
98C22⋊(C59⋊C8)—22no—
99C22⋊(C59⋊C8)—41no—
100C4×C59⋊C8—22no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C25×C59—21no—
106C22×D4×C59—22no—
107C22×D4×C59—22no—
108C22×D4×C59—22no—
109C22×D4×C59—22no—
110C22×D4×C59—21no—
111C22×D4×C59—41no—
112C22×D4×C59—41no—
113C22×D4×C59C2311yescharacteristic
114C22×D4×C59C2311yescharacteristic
115C23×C4×C59—21no—
116C23×C4×C59—21no—
117C23×C4×C59C2311yescharacteristic
118C4×D4×C59—22no—
119C4×D4×C59—22no—
120C4×D4×C59—41no—
121C4×D4×C59—41no—
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C22⋊C4×C59—21no—
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×C22⋊C4×C59—44no—
132C2×C22⋊C4×C59D411yescharacteristic
133C2×C22⋊C4×C59D411yescharacteristic
134C2×C42×C59C2311yescharacteristic
135C2×C42×C59C2311yescharacteristic
136#95×C59—21no—
137#95×C59D411yescharacteristic
138#95×C59D411yescharacteristic
139C24×C59—21no—
140C24×C59—24no—
141C24×C59—21no—
142C24×C59—42no—
143C24×C59—42no—
144C24×C59—42no—
145C24×C59—42no—
146C24×C59—81no—
147C24×C59—81no—
148C24×C59C2×D411yescharacteristic
149C2×D4×C59—24no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—42no—
159C2×D4×C59—42no—
160C2×D4×C59—44no—
161C2×D4×C59—44no—
162C2×D4×C59—44no—
163C2×D4×C59—44no—
164C2×D4×C59C2×D412yes—
165C2×D4×C59#4112yes—
166C2×D4×C59#4112yes—
167C2×D4×C59#4112yes—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—42no—
177C22×C4×C59—42no—
178C22×C4×C59—42no—
179C22×C4×C59—42no—
180C22×C4×C59—81no—
181C22×C4×C59—81no—
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2411yescharacteristic
188C22×Dic59—21no—
189C22×Dic59—21no—
190C22×Dic59—21no—
191C22×Dic59—21no—
192C2×Dic118—21no—
193C2×Dic118—21no—
194C2×Dic118—21no—
195C2×Dic118—21no—
196C2×Dic118—21no—
197C2×Dic118C2×D412yes—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C22⋊C4×C59—41no—
203C22⋊C4×C59—42no—
204C22⋊C4×C59—42no—
205C22⋊C4×C59—42no—
206C22⋊C4×C59—42no—
207C22⋊C4×C59—42no—
208C22⋊C4×C59—81no—
209C22⋊C4×C59—81no—
210C22⋊C4×C59SD1614yescomplemented
211C42×C59—21no—
212C42×C59—21no—
213C42×C59—21no—
214C42×C59—21no—
215C22⋊Dic59—42no—
216C22⋊Dic59—81no—
217#11745670—28no—
218#11745670—44no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—42no—
226C4⋊Dic59—81no—
227Dic59⋊C4—42no—
228Dic59⋊C4—42no—
229Dic59⋊C4—81no—
230C4×Dic59—42no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8C2×D412yes—
243C23×C59—21no—
244C23×C59—22no—
245C23×C59—21no—
246C23×C59—22no—
247C23×C59—22no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—22no—
253C23×C59—48no—
254C23×C59—48no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—84no—
266C23×C59—84no—
267C23×C59—84no—
268C23×C59—84no—
269C23×C59—84no—
270C23×C59C2×SD1612yes—
271C23×C59C22×D411yescharacteristic
272D4×C59—22no—
273D4×C59—22no—
274D4×C59—22no—
275D4×C59—22no—
276D4×C59—22no—
277D4×C59—48no—
278D4×C59—41no—
279D4×C59—41no—
280D4×C59#12314yes—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—84no—
305C2×C4×C59—84no—
306C2×C4×C59C2×SD1612yes—
307C2×C4×C59C2×SD1612yes—
308C2×C4×C59C22×D411yescharacteristic
309C2×C4×C59C2×#4111yescharacteristic
310C2×C4×C59C2×#4111yescharacteristic
311C2×C4×C59C2×#4111yescharacteristic
312C2×C4×C59H(5,𝔽2)11yescharacteristic
313C2×C4×C59H(5,𝔽2)11yescharacteristic
314C2×Dic59—22no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326Dic118—22no—
327Dic118—22no—
328Dic118—41no—
329Dic118—41no—
330C59⋊C8—22no—
331C59⋊C8—41no—
332C59⋊C8—41no—
333C59⋊C8—41no—
334#24901—591nomaximal, Sylow
335C22×C59—22no—
336C22×C59—24no—
337C22×C59—22no—
338C22×C59—22no—
339C22×C59—42no—
340C22×C59—41no—
341C22×C59—42no—
342C22×C59—41no—
343C22×C59—41no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—41no—
348C22×C59—42no—
349C22×C59—42no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—816no—
353C22×C59—81no—
354C22×C59—81no—
355C22×C59—81no—
356C22×C59—81no—
357C22×C59#52511yescharacteristic
358C22×C59D4211yescharacteristic
359C22×C59#54611yescharacteristic
360C22×C59C22×SD1611yescharacteristic
361C22×C59#57511yescharacteristic
362C22×C59#57611yescharacteristic
363C22×C59#57711yescharacteristic
364C4×C59—22no—
365C4×C59—22no—
366C4×C59—41no—
367C4×C59—41no—
368C4×C59—41no—
369C4×C59—81no—
370C4×C59—81no—
371C4×C59C2×#12311yescharacteristic
372C4×C59#53811yescharacteristic
373C4×C59#54611yescharacteristic
374C4×C59#55111yescharacteristic
375Dic59—42no—
376Dic59—81no—
377Dic59—81no—
378Dic59—81no—
379C2×#450—591no—
380C2×C4×SD16—591no—
381#2423—591no—
382D4×C22⋊C4D5911yescharacteristic
383#2094—591no—
384#2077—591no—
385#2055—591no—
386#2035—591no—
387#1934—591no—
388#1923—591no—
389#1880—591no—
390#1877—591no—
391#1864—591no—
392#1802—591no—
393#1786—591no—
394C2×C59—42no—
395C2×C59—44no—
396C2×C59—82no—
397C2×C59#241811yescharacteristic
398C2×C59#310111yescharacteristic
399C2×C59#311811yescharacteristic
400C2×C59#326811yescharacteristic
401C2×C59D4×SD1611yescharacteristic
402C2×C59#329511yescharacteristic
403C2×C59#332311yescharacteristic
404C23×D4C2×D5911yescharacteristic
405C22×SD16—591no—
406C22×SD16—591no—
407C2×C22⋊Q8—591no—
408C2×C4×Q8—591no—
409C2×C4×D4C2×D5911yescharacteristic
410C2×C4×D4C2×D5911yescharacteristic
411C22×C22⋊C4—21no—
412#450—1184no—
413C4×SD16—1184no—
414C2×#106—591no—
415C2×#106—591no—
416C2×C4⋊C8—591no—
417C2×#103—591no—
418C2×#103—591no—
419C2×#102—591no—
420C2×#102—591no—
421C2×#102—591no—
422C2×#102—591no—
423C2×#102—591no—
424C2×#102—591no—
425C2×C22⋊C8—591no—
426C2×C22⋊C8—591no—
427C2×C4×C8—591no—
428#399—1181no—
429#398—1181no—
430#391—591no—
431#390C2×D5911yescharacteristic
432#390C2×D5911yescharacteristic
433#389—591no—
434#388—1181no—
435#387—1181no—
436#386—21no—
437#386—21no—
438#384—591no—
439#380—591no—
440#380C2×D5911yescharacteristic
441#379—21no—
442C4×C22⋊C4C2×D5911yescharacteristic
443#340—591no—
444#340—591no—
445#340—591no—
446#340—591no—
447#336—591no—
448#336—591no—
449C59#2490111yescharacteristic, complemented, Sylow
450C25—21no—
451C22×Q8—591no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C22×D5911yescharacteristic
460C22×D4C22×D5911yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C22×D5911yescharacteristic
464C2×SD16—594no—
465C2×SD16—1182no—
466C2×SD16—1182no—
467C2×SD16—1182no—
468C2×SD16—1182no—
469C2×SD16—2361no—
470C22×C8—591no—
471C22×C8—591no—
472C22×C8—591no—
473C22×C8—591no—
474C22⋊Q8—1182no—
475C22⋊Q8—2361no—
476C4×Q8—1182no—
477C4×Q8—2361no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4—1181no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4C22×D5911yescharacteristic
491C2×C4⋊C4C22×D5911yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—44no—
500C2×C22⋊C4—1181no—
501C2×C22⋊C4—1181no—
502C2×C22⋊C4C22⋊D5911yescharacteristic
503C2×C22⋊C4C22⋊D5911yescharacteristic
504C2×C42—1181no—
505C2×C42C22×D5911yescharacteristic
506C2×C42C22×D5911yescharacteristic
507#106—1182no—
508#106—2361no—
509C4⋊C8—2361no—
510#103—1182no—
511#103—2361no—
512#102—1182no—
513#102—1182no—
514#102—1182no—
515#102—1182no—
516#102—1182no—
517#102—2361no—
518C22⋊C8—1182no—
519C22⋊C8—2361no—
520C4×C8—1182no—
521#95—21no—
522#95—1181no—
523#95—1181no—
524#95—1181no—
525#95—1181no—
526#95C22⋊D5911yescharacteristic
527#95C22⋊D5911yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×C22⋊D5911yescharacteristic
538C2×Q8—592no—
539C2×Q8—1181no—
540C2×Q8—1181no—
541C2×Q8—1181no—
542C2×Q8—1181no—
543C2×Q8—1181no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4#1174568512yes—
560C2×D4#1174568512yes—
561C2×D4D4×D5912yes—
562C2×D4#1174568712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4C2×C22⋊D5911yescharacteristic
582C22×C4C2×C22⋊D5911yescharacteristic
583C22×C4C2×C22⋊D5911yescharacteristic
584C22×C4C2×C22⋊D5911yescharacteristic
585C22×C4C2×C22⋊D5911yescharacteristic
586C22×C4C23×D5911yescharacteristic
587SD16—1188no—
588SD16—2364no—
589C2×C8—592no—
590C2×C8—1181no—
591C2×C8—1181no—
592C2×C8—1181no—
593C2×C8—1181no—
594C2×C8—1181no—
595C2×C8—1181no—
596C2×C8—1181no—
597C2×C8—1181no—
598C2×C8—1181no—
599C2×C8—1181no—
600C2×C8—1181no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—1181no—
606C4⋊C4—1181no—
607C4⋊C4—1181no—
608C4⋊C4—1181no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—4721no—
612C4⋊C4—4721no—
613C4⋊C4—2362no—
614C4⋊C4—2362no—
615C4⋊C4—2362no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—4721no—
625C22⋊C4—2362no—
626C22⋊C4#1174567014yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—2362no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×#1174567012yes—
660C23C22×C22⋊D5911yescharacteristic
661Q8—1182no—
662Q8—1182no—
663Q8—2361no—
664Q8—2361no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#1427370914yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—1182no—
700C2×C4—2361no—
701C2×C4—2361no—
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×C4C2×#1174567012yes—
712C2×C4C2×#1174567012yes—
713C2×C4C2×D4×D5911yescharacteristic
714C2×C4C2×#1174568711yescharacteristic
715C2×C4C2×#1174568511yescharacteristic
716C2×C4C2×#1174568511yescharacteristic
717C2×C4#1427377211yescharacteristic
718C2×C4#1427377211yescharacteristic
719C8—1182no—
720C8—2361no—
721C8—2361no—
722C8—2361no—
723C22—22no—
724C22—24no—
725C22—22no—
726C22—22no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#1683791311yescharacteristic
746C22D4×C22⋊D5911yescharacteristic
747C22#1683804611yescharacteristic
748C22C22×#1174567011yescharacteristic
749C22#1683820011yescharacteristic
750C22#1683820511yescharacteristic
751C22#1683821311yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—81no—
758C4—81no—
759C4—4721no—
760C4—4721no—
761C4—4721no—
762C4—2362no—
763C4C2×#1427370911yescharacteristic
764C4#1683799011yescharacteristic
765C4#1683804211yescharacteristic
766C4#1683807811yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2#2142755811yescharacteristic
771C2#2143410411yescharacteristic
772C2#2143428011yescharacteristic
773C2#2143563211yescharacteristic
774C2D4×#1174567011yescharacteristic
775C2#2143592011yescharacteristic
776C2#2143631211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingD4×C22⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC23×D4×C59C22
hypercenterD4×C22⋊C4D59
hypocenterC59#24901
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745670C2semidirect
3. #21427621C2semidirect
4. #21425629C2semidirect
5. #21425532C2semidirect
6. #21425413C2semidirect
7. #21425292C2semidirect
8. #21424782C2semidirect
9. #21424704C2semidirect
10. #21424454C2semidirect
11. #21424430C2semidirect
12. #21424357C2semidirect
13. #21424096C2semidirect
19. C2×C4×Dic118C22semidirect
22. C2×#14273658C22semidirect
23. C2×#14273658C22semidirect
24. C2×C4⋊(C59⋊C8)C22semidirect
25. C2×#14273650C22semidirect
26. C2×#14273650C22semidirect
35. C2×C4×C59⋊C8C22semidirect
38. #16837308C22semidirect
39. #16837300C22semidirect
42. #16837272C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
48. #16837157C22semidirect
49. #16837157C22semidirect
210. C22⋊C4×C59SD16semidirect
449. C59#24901semidirect
626. C22⋊C4#11745670semidirect

Maximal subgroups

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

subgroupindex
C2×#168375532
C2×C4×#117456702
#214276212
#214256292
#214255322
#214254132
#214252922
#214247822
#214247042
#214244542
#214244302
#214243572
#214240962
#214240272
D4×C22⋊C4×C592
#2490159