Finite Group Databasebeta

← #28495194

Subgroups — #28495194

Order 15104.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273698C211yesmaximal, characteristic
2C22×#14273648C211yesmaximal, characteristic, complemented
3C22×(C2×D59)⋊C8C211yesmaximal, characteristic, complemented
4C2×#16837259C211yesmaximal, characteristic, complemented
5C2×#16837165C211yesmaximal, characteristic, complemented
6C2×#16837164C211yesmaximal, characteristic, complemented
7C22×#102×C59C211yesmaximal, characteristic, complemented
8C23×C22⋊D59—21no—
9C23×C4×D59C2211yescharacteristic
10C23×C59⋊C8C2211yescharacteristic
11C2×#14273698—22no—
12C2×#14273698—22no—
13C2×#14273698—22no—
14C2×#14273698—22no—
15C2×#14273698—22no—
16C2×#14273698C414yescomplemented
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C22⋊Dic59—21no—
20C22×(C2×D59)⋊C4—21no—
21C2×#14273648—22no—
22C2×#14273648—22no—
23C2×#14273648—22no—
24C2×(C2×D59)⋊C8—22no—
25C2×(C2×D59)⋊C8—22no—
26C2×(C2×D59)⋊C8—22no—
27#16837259—22no—
28#16837259—22no—
29C2×C59⋊#95—21no—
30#16837165—22no—
31#16837164—22no—
32C23×D4×C59C2211yescharacteristic
33C23×C8×C59C2211yescharacteristic
34C22×C4⋊C4×C59C2211yescharacteristic
35C2×#102×C59—22no—
36C2×#102×C59—22no—
37C2×#102×C59—22no—
38C24×D59D411yescharacteristic
39C22×C22⋊D59—24no—
40C22×C22⋊D59—24no—
41C22×C22⋊D59—24no—
42C22×C22⋊D59—42no—
43C22×C22⋊D59—42no—
44C22×C22⋊D59—42no—
45C22×C22⋊D59—42no—
46C23×Dic59—21no—
47C23×Dic59—21no—
48C23×Dic59D411yescharacteristic
49C22×C4×D59—21no—
50C22×C4×D59—21no—
51C22×C4×D59—21no—
52C22×C4×D59—21no—
53C22×C4×D59—21no—
54C22×C4×D59—21no—
55C22×C4×D59—21no—
56C22×C4×D59—21no—
57C22×C4×D59—21no—
58C22×C4×D59—21no—
59C22×C4×D59—21no—
60C22×C4×D59—21no—
61C22×C4×D59C2×C412yes—
62C22×C4×D59D412yes—
63C22×C59⋊C8—21no—
64C22×C59⋊C8—21no—
65C22×C59⋊C8—21no—
66C22×C59⋊C8—21no—
67C22×C59⋊C8—21no—
68C22×C59⋊C8—21no—
69C22×C59⋊C8D412yescomplemented
70#14273698—28no—
71#14273698—28no—
72#14273698—28no—
73#14273698—28no—
74C2×C4⋊Dic59—21no—
75C2×C4⋊Dic59—21no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59—21no—
80C2×C4⋊Dic59—21no—
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59C2×C412yes—
83C2×C4⋊Dic59D412yes—
84C2×C4⋊Dic59D412yes—
85C2×C4⋊Dic59D412yescomplemented
86C2×C22⋊Dic59—24no—
87C2×C22⋊Dic59—24no—
88C2×C22⋊Dic59—24no—
89C2×(C2×D59)⋊C4—24no—
90C2×(C2×D59)⋊C4—42no—
91C2×(C2×D59)⋊C4—42no—
92#14273648—28no—
93(C2×D59)⋊C8—28no—
94C59⋊#95—24no—
95C25×C59—21no—
96C22×D4×C59—21no—
97C22×D4×C59—21no—
98C22×D4×C59—21no—
99C22×D4×C59—21no—
100C22×D4×C59—21no—
101C22×D4×C59—21no—
102C22×D4×C59—21no—
103C22×D4×C59—21no—
104C22×D4×C59—21no—
105C22×D4×C59—21no—
106C22×D4×C59—21no—
107C22×D4×C59C2×C412yes—
108C22×D4×C59D412yes—
109C22×D4×C59D412yes—
110C23×C4×C59—21no—
111C23×C4×C59C2311yescharacteristic
112C22×C8×C59—21no—
113C22×C8×C59—21no—
114C22×C8×C59—21no—
115C22×C8×C59—21no—
116C22×C8×C59—21no—
117C22×C8×C59—21no—
118C22×C8×C59D412yescomplemented
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—21no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59D412yescomplemented
125#102×C59—28no—
126C24×C59—22no—
127C24×C59—22no—
128C24×C59—22no—
129C24×C59—41no—
130C24×C59—41no—
131C24×C59—41no—
132C24×C59—41no—
133C24×C59—41no—
134C24×C59—41no—
135C24×C59—41no—
136C24×C59—41no—
137C24×C59—41no—
138C24×C59—41no—
139C24×C59—41no—
140C24×C59—41no—
141C24×C59C2×D411yescharacteristic
142C23×D59—21no—
143C23×D59—21no—
144C23×D59—21no—
145C23×D59—21no—
146C23×D59—21no—
147C23×D59—21no—
148C23×D59—21no—
149C23×D59—21no—
150C23×D59—21no—
151C23×D59—21no—
152C23×D59—21no—
153C23×D59—21no—
154C23×D59C22⋊C412yes—
155C23×D59D812yes—
156C23×D59SD1612yes—
157C2×D4×C59—22no—
158C2×D4×C59—22no—
159C2×D4×C59—22no—
160C2×D4×C59—22no—
161C2×D4×C59—22no—
162C2×D4×C59—22no—
163C2×D4×C59—22no—
164C2×D4×C59—22no—
165C2×D4×C59—22no—
166C2×D4×C59—22no—
167C2×D4×C59—22no—
168C2×D4×C59—22no—
169C2×D4×C59—22no—
170C2×D4×C59—22no—
171C2×D4×C59—22no—
172C2×D4×C59—41no—
173C2×D4×C59—41no—
174C2×D4×C59—41no—
175C2×D4×C59—41no—
176C2×D4×C59—41no—
177C2×D4×C59—41no—
178C2×D4×C59—41no—
179C2×D4×C59—41no—
180C2×D4×C59—41no—
181C2×D4×C59—41no—
182C2×D4×C59—41no—
183C2×D4×C59—41no—
184C2×D4×C59C22⋊C414yescomplemented
185C22×C4×C59—22no—
186C22×C4×C59—41no—
187C22×C4×C59—41no—
188C22×C4×C59—41no—
189C22×C4×C59—41no—
190C22×C4×C59—41no—
191C22×C4×C59—41no—
192C22×C4×C59C22×C411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59#4111yescharacteristic
203C22×C4×C59#4111yescharacteristic
204C22×C4×C59#4111yescharacteristic
205C22×C4×C59#4111yescharacteristic
206C2×C22⋊D59—216no—
207C2×C22⋊D59—48no—
208C2×C22⋊D59—48no—
209C2×C22⋊D59—48no—
210C2×C22⋊D59—48no—
211C2×C22⋊D59—48no—
212C2×C22⋊D59—48no—
213C22×Dic59—22no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—22no—
218C22×Dic59—22no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—22no—
223C22×Dic59—41no—
224C22×Dic59—41no—
225C22×Dic59—41no—
226C22×Dic59—41no—
227C22×Dic59—41no—
228C22×Dic59—41no—
229C22×Dic59—41no—
230C22×Dic59—41no—
231C22×Dic59—41no—
232C22×Dic59—41no—
233C22×Dic59C22⋊C412yes—
234C2×C4×D59—22no—
235C2×C4×D59—22no—
236C2×C4×D59—22no—
237C2×C4×D59—22no—
238C2×C4×D59—22no—
239C2×C4×D59—22no—
240C2×C4×D59—22no—
241C2×C4×D59—22no—
242C2×C4×D59—22no—
243C2×C4×D59—22no—
244C2×C4×D59—22no—
245C2×C4×D59—22no—
246C2×C4×D59—41no—
247C2×C4×D59—41no—
248C2×C4×D59—41no—
249C2×C4×D59—41no—
250C2×C4×D59—41no—
251C2×C4×D59—41no—
252C2×C4×D59—41no—
253C2×C4×D59—41no—
254C2×C4×D59—41no—
255C2×C4×D59—41no—
256C2×C4×D59—41no—
257C2×C4×D59—41no—
258C2×C4×D59—41no—
259C2×C4×D59—41no—
260C2×C4×D59—41no—
261C2×C4×D59—41no—
262C2×C8×C59—22no—
263C2×C8×C59—22no—
264C2×C8×C59—22no—
265C2×C8×C59—41no—
266C2×C8×C59—41no—
267C2×C8×C59—41no—
268C2×C8×C59—41no—
269C4⋊C4×C59—22no—
270C4⋊C4×C59—22no—
271C4⋊C4×C59—41no—
272C4⋊C4×C59—41no—
273C22⋊Dic59—216no—
274(C2×D59)⋊C4—48no—
275C4⋊Dic59—22no—
276C4⋊Dic59—22no—
277C4⋊Dic59—22no—
278C4⋊Dic59—22no—
279C4⋊Dic59—22no—
280C4⋊Dic59—41no—
281C4⋊Dic59—41no—
282C4⋊Dic59C22⋊C414yescomplemented
283C2×C59⋊C8—22no—
284C2×C59⋊C8—22no—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—41no—
287C2×C59⋊C8—41no—
288C2×C59⋊C8—41no—
289C2×C59⋊C8—41no—
290C23×C59—24no—
291C23×C59—42no—
292C23×C59—42no—
293C23×C59—42no—
294C23×C59—42no—
295C23×C59—42no—
296C23×C59—42no—
297C23×C59—42no—
298C23×C59—42no—
299C23×C59—42no—
300C23×C59—42no—
301C23×C59—42no—
302C23×C59—42no—
303C23×C59—42no—
304C23×C59—42no—
305C23×C59—42no—
306C23×C59—42no—
307C23×C59—42no—
308C23×C59—42no—
309C23×C59—81no—
310C23×C59—81no—
311C23×C59—81no—
312C23×C59—81no—
313C23×C59—81no—
314C23×C59—81no—
315C23×C59—81no—
316C23×C59—81no—
317C23×C59—81no—
318C23×C59—81no—
319C23×C59—81no—
320C23×C59—81no—
321C23×C59—81no—
322C23×C59—81no—
323C23×C59—81no—
324C23×C59—81no—
325C23×C59C2×C22⋊C411yescharacteristic
326C23×C59#12011yescharacteristic
327C23×C59#12011yescharacteristic
328C23×C59#12011yescharacteristic
329C23×C59#12111yescharacteristic
330C23×C59#12111yescharacteristic
331C23×C59#12311yescharacteristic
332C23×C59C2×D811yescharacteristic
333C23×C59C2×SD1611yescharacteristic
334C23×C59#13511yescharacteristic
335C23×C59#13511yescharacteristic
336C23×C59AGL(1,ℤ/8)11yescharacteristic
337C23×C59AGL(1,ℤ/8)11yescharacteristic
338C23×C59AGL(1,ℤ/8)11yescharacteristic
339C23×C59#13711yescharacteristic
340C22×D59—22no—
341C22×D59—22no—
342C22×D59—22no—
343C22×D59—22no—
344C22×D59—22no—
345C22×D59—22no—
346C22×D59—22no—
347C22×D59—22no—
348C22×D59—22no—
349C22×D59—22no—
350C22×D59—22no—
351C22×D59—22no—
352C22×D59—22no—
353C22×D59—22no—
354C22×D59—22no—
355C22×D59—22no—
356C22×D59—22no—
357C22×D59—22no—
358C22×D59—41no—
359C22×D59—41no—
360C22×D59—41no—
361C22×D59—41no—
362C22×D59—41no—
363C22×D59—41no—
364C22×D59—41no—
365C22×D59—41no—
366C22×D59—41no—
367C22×D59—41no—
368C22×D59—41no—
369C22×D59—41no—
370C22×D59—41no—
371C22×D59—41no—
372C22×D59—41no—
373C22×D59—41no—
374C22×D59#10214yescomplemented
375D4×C59—24no—
376D4×C59—24no—
377D4×C59—42no—
378D4×C59—42no—
379D4×C59—42no—
380D4×C59—42no—
381D4×C59—42no—
382D4×C59—42no—
383C2×C4×C59—42no—
384C2×C4×C59—42no—
385C2×C4×C59—42no—
386C2×C4×C59—81no—
387C2×C4×C59—81no—
388C2×C4×C59—81no—
389C2×C4×C59—81no—
390C2×C4×C59C2×C22⋊C411yescharacteristic
391C2×C4×C59C2×C22⋊C411yescharacteristic
392C2×C4×C59C4×D411yescharacteristic
393C2×C4×C59C4×D411yescharacteristic
394C2×C4×C59C4×D411yescharacteristic
395C2×C4×C59C4×D411yescharacteristic
396C2×C4×C59#12011yescharacteristic
397C2×C4×C59#12011yescharacteristic
398C2×C4×C59#12011yescharacteristic
399C2×C4×C59#12011yescharacteristic
400C2×C4×C59#12011yescharacteristic
401C2×C4×C59#12111yescharacteristic
402C2×C4×C59#12111yescharacteristic
403C2×C4×C59#12111yescharacteristic
404C2×C4×C59#12111yescharacteristic
405C2×C4×C59#12111yescharacteristic
406C2×C4×C59#12111yescharacteristic
407C2×C4×C59#12111yescharacteristic
408C2×C4×C59#12111yescharacteristic
409C2×C4×C59#12111yescharacteristic
410C2×C4×C59#12111yescharacteristic
411C2×C4×C59#12311yescharacteristic
412C2×C4×C59#12311yescharacteristic
413C2×C4×C59#12311yescharacteristic
414C2×C4×C59#12411yescharacteristic
415C2×C4×C59#12411yescharacteristic
416C2×C4×C59#12711yescharacteristic
417C2×C4×C59#12711yescharacteristic
418C22⋊D59—432no—
419C2×Dic59—24no—
420C2×Dic59—22no—
421C2×Dic59—22no—
422C2×Dic59—22no—
423C2×Dic59—41no—
424C2×Dic59—41no—
425C2×Dic59—41no—
426C2×Dic59—41no—
427C2×Dic59—42no—
428C2×Dic59—42no—
429C2×Dic59—42no—
430C2×Dic59—42no—
431C2×Dic59—42no—
432C2×Dic59—42no—
433C2×Dic59—42no—
434C2×Dic59—42no—
435C2×Dic59—42no—
436C2×Dic59—81no—
437C2×Dic59—81no—
438C2×Dic59—81no—
439C2×Dic59—81no—
440C4×D59—42no—
441C4×D59—42no—
442C4×D59—42no—
443C4×D59—42no—
444C4×D59—42no—
445C4×D59—42no—
446C4×D59—42no—
447C4×D59—42no—
448C8×C59—42no—
449C59⋊C8—42no—
450#10969—591nomaximal, Sylow
451C22×C59—44no—
452C22×C59—44no—
453C22×C59—44no—
454C22×C59—82no—
455C22×C59—82no—
456C22×C59—82no—
457C22×C59—82no—
458C22×C59—82no—
459C22×C59—82no—
460C22×C59—82no—
461C22×C59—82no—
462C22×C59—82no—
463C22×C59—82no—
464C22×C59—82no—
465C22×C59—82no—
466C22×C59#37911yescharacteristic
467C22×C59#38611yescharacteristic
468C22×C59#38611yescharacteristic
469C22×C59#39211yescharacteristic
470C22×C59#39211yescharacteristic
471C22×C59#39411yescharacteristic
472C22×C59#39411yescharacteristic
473C22×C59C2×#10211yescharacteristic
474C22×C59#41611yescharacteristic
475C22×C59#41711yescharacteristic
476C22×C59#41811yescharacteristic
477C22×C59#44711yescharacteristic
478C22×C59#44711yescharacteristic
479C22×C59#44711yescharacteristic
480C22×C59#44811yescharacteristic
481C22×C59#44911yescharacteristic
482C22×C59#44911yescharacteristic
483C22×C59#44911yescharacteristic
484C22×C59#44911yescharacteristic
485C22×C59#45011yescharacteristic
486C22×C59#45011yescharacteristic
487C22×C59#45211yescharacteristic
488C22×C59#45211yescharacteristic
489C22×C59#46511yescharacteristic
490C22×C59#46511yescharacteristic
491C22×C59#46611yescharacteristic
492C22×C59#46611yescharacteristic
493C22×C59#46811yescharacteristic
494C22×C59#46811yescharacteristic
495C22×C59#46911yescharacteristic
496C22×C59#46911yescharacteristic
497C22×C59#48011yescharacteristic
498C22×C59#48111yescharacteristic
499C22×C59#48211yescharacteristic
500C22×C59#48211yescharacteristic
501C2×D59—24no—
502C2×D59—24no—
503C2×D59—24no—
504C2×D59—42no—
505C2×D59—42no—
506C2×D59—42no—
507C2×D59—42no—
508C2×D59—42no—
509C2×D59—42no—
510C2×D59—42no—
511C2×D59—42no—
512C2×D59—42no—
513C2×D59—42no—
514C2×D59—42no—
515C2×D59—42no—
516C4×C59—82no—
517C4×C59#38611yescharacteristic
518C4×C59#38611yescharacteristic
519C4×C59#39011yescharacteristic
520C4×C59#39011yescharacteristic
521C4×C59#39211yescharacteristic
522C4×C59#39211yescharacteristic
523C4×C59#39411yescharacteristic
524C4×C59#39411yescharacteristic
525Dic59—42no—
526Dic59—44no—
527Dic59—82no—
528C22×#121—591no—
529C22×#102—591no—
530C22×#102D5911yescharacteristic, complemented
531C22×C22⋊C8—591no—
532C2×#380—591no—
533C2×#340—591no—
534C2×#340—591no—
535C2×C59—84no—
536C2×C59#143811yescharacteristic
537C2×C59#178611yescharacteristic
538C2×C59#178811yescharacteristic
539C2×C59#187411yescharacteristic
540C2×C59#187511yescharacteristic
541C2×C59#189311yescharacteristic
542C2×C59#189511yescharacteristic
543C2×C59#199911yescharacteristic
544C2×C59#199911yescharacteristic
545C2×C59#200011yescharacteristic
546C2×C59#200011yescharacteristic
547C2×C59#203311yescharacteristic
548C2×C59#203311yescharacteristic
549C2×C59#203411yescharacteristic
550C2×C59#203411yescharacteristic
551D59—44no—
552C23×D4—1181no—
553C23×D4C2×D5911yescharacteristic
554C24×C4—591no—
555C23×C8—591no—
556C23×C8C2×D5911yescharacteristic
557C2×#121—594no—
558C2×#121—1182no—
559C2×#121—1182no—
560C2×#121—1182no—
561C2×#121—1182no—
562C2×#121—1182no—
563C22×C4⋊C4—591no—
564C22×C4⋊C4—591no—
565C22×C4⋊C4C2×D5911yescharacteristic
566C22×C22⋊C4—1181no—
567C22×C22⋊C4—1181no—
568C2×#102—22no—
569C2×#102—22no—
570C2×#102—22no—
571C2×#102—1182no—
572C2×#102—1182no—
573C2×#102—1182no—
574C2×C22⋊C8—1182no—
575C2×C22⋊C8—1182no—
576C2×C22⋊C8—1182no—
577#380—1182no—
578#380—1182no—
579C2×#95—1181no—
580#340—1182no—
581#340—1182no—
582C59#1096911yescharacteristic, complemented, Sylow
583C25—21no—
584C25—591no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—1184no—
597C22×D4—1184no—
598C22×D4—1184no—
599C22×D4—2362no—
600C22×D4—2362no—
601C22×D4—2362no—
602C22×D4—2362no—
603C22×D4C4×D5912yes—
604C22×D4D23612yes—
605C22×D4C22⋊D5912yes—
606C23×C4—21no—
607C23×C4—591no—
608C23×C4—592no—
609C23×C4—592no—
610C23×C4—1181no—
611C23×C4—1181no—
612C23×C4—1181no—
613C23×C4—1181no—
614C23×C4—1181no—
615C23×C4—1181no—
616C23×C4—1181no—
617C23×C4—1181no—
618C23×C4—1181no—
619C23×C4—1181no—
620C23×C4—1181no—
621C23×C4—1181no—
622C23×C4—1181no—
623C23×C4—1181no—
624C23×C4C22×D5911yescharacteristic
625C22×C8—21no—
626C22×C8—21no—
627C22×C8—21no—
628C22×C8—21no—
629C22×C8—21no—
630C22×C8—21no—
631C22×C8—592no—
632C22×C8—1181no—
633C22×C8—1181no—
634C22×C8—1181no—
635C22×C8—1181no—
636C22×C8—1181no—
637C22×C8—1181no—
638C22×C8C22⋊D5912yescomplemented
639#121—1188no—
640#121—1188no—
641#121—1188no—
642#121—1188no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—592no—
649C2×C4⋊C4—592no—
650C2×C4⋊C4—592no—
651C2×C4⋊C4—592no—
652C2×C4⋊C4—1181no—
653C2×C4⋊C4—1181no—
654C2×C4⋊C4—1181no—
655C2×C4⋊C4—1181no—
656C2×C4⋊C4—1181no—
657C2×C4⋊C4—1181no—
658C2×C4⋊C4—1181no—
659C2×C4⋊C4—1181no—
660C2×C4⋊C4C22⋊D5912yescomplemented
661C2×C22⋊C4—1184no—
662C2×C22⋊C4—1184no—
663C2×C22⋊C4—1184no—
664C2×C22⋊C4—1184no—
665C2×C22⋊C4—2362no—
666C2×C22⋊C4—2362no—
667#102—28no—
668#102—1188no—
669C22⋊C8—1188no—
670#95—1184no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—41no—
675C24—41no—
676C24—41no—
677C24—41no—
678C24—41no—
679C24—41no—
680C24—41no—
681C24—41no—
682C24—41no—
683C24—41no—
684C24—41no—
685C24—41no—
686C24—592no—
687C24—592no—
688C24—592no—
689C24—1181no—
690C24—1181no—
691C24—1181no—
692C24—1181no—
693C24—1181no—
694C24—1181no—
695C24—1181no—
696C24—1181no—
697C24—1181no—
698C24—1181no—
699C24—1181no—
700C24—1181no—
701C24D4×D5911yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—41no—
723C2×D4—41no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—41no—
728C2×D4—41no—
729C2×D4—11816no—
730C2×D4—2368no—
731C2×D4—2368no—
732C2×D4—2368no—
733C2×D4—2368no—
734C2×D4—2368no—
735C2×D4—2368no—
736C2×D4(C2×D59)⋊C414yescomplemented
737C22×C4—22no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—592no—
745C22×C4—1182no—
746C22×C4—1181no—
747C22×C4—1181no—
748C22×C4—1182no—
749C22×C4—1181no—
750C22×C4—1182no—
751C22×C4—1181no—
752C22×C4—1181no—
753C22×C4—1181no—
754C22×C4—1182no—
755C22×C4—1182no—
756C22×C4—1182no—
757C22×C4—1182no—
758C22×C4—1182no—
759C22×C4—1182no—
760C22×C4—1182no—
761C22×C4—1182no—
762C22×C4—1182no—
763C22×C4—1182no—
764C22×C4—1182no—
765C22×C4—1182no—
766C22×C4—1182no—
767C22×C4—2361no—
768C22×C4—2361no—
769C22×C4—2361no—
770C22×C4—2361no—
771C22×C4—2361no—
772C22×C4—2361no—
773C22×C4—2361no—
774C22×C4—2361no—
775C22×C4—2361no—
776C22×C4—2361no—
777C22×C4—2361no—
778C22×C4—2361no—
779C22×C4—2361no—
780C22×C4—2361no—
781C22×C4—2361no—
782C22×C4—2361no—
783C22×C4—2361no—
784C22×C4—2361no—
785C22×C4—2361no—
786C22×C4—2361no—
787C22×C4—2361no—
788C22×C4—2361no—
789C22×C4—2361no—
790C22×C4—2361no—
791C22×C4—2361no—
792C22×C4—2361no—
793C22×C4C2×C4×D5911yescharacteristic
794C22×C4C2×D23611yescharacteristic
795C22×C4#1174568511yescharacteristic
796C22×C4#1174568511yescharacteristic
797C22×C4D4×D5911yescharacteristic
798C22×C4D4×D5911yescharacteristic
799C22×C4D4×D5911yescharacteristic
800C22×C4D4×D5911yescharacteristic
801C22×C4D4×D5911yescharacteristic
802C22×C4#1174568711yescharacteristic
803C22×C4#1174568711yescharacteristic
804C22×C4C2×C22⋊D5911yescharacteristic
805C22×C4C2×C22⋊D5911yescharacteristic
806C22×C4C2×C22⋊D5911yescharacteristic
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—22no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8—41no—
814C2×C8—1182no—
815C2×C8—1182no—
816C2×C8—1182no—
817C2×C8—2361no—
818C2×C8—2361no—
819C2×C8—2361no—
820C2×C8—2361no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—41no—
824C4⋊C4—41no—
825C4⋊C4—594no—
826C4⋊C4—1182no—
827C4⋊C4—1182no—
828C4⋊C4—1182no—
829C4⋊C4—1182no—
830C4⋊C4—1182no—
831C4⋊C4—2361no—
832C4⋊C4—2361no—
833C22⋊C4—11816no—
834C22⋊C4—2368no—
835C23—24no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—81no—
855C23—81no—
856C23—81no—
857C23—81no—
858C23—81no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23—81no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23—81no—
870C23—594no—
871C23—1182no—
872C23—1182no—
873C23—1182no—
874C23—1182no—
875C23—1182no—
876C23—1182no—
877C23—1182no—
878C23—1182no—
879C23—1182no—
880C23—1182no—
881C23—1182no—
882C23—1182no—
883C23—1182no—
884C23—1182no—
885C23—1182no—
886C23—1182no—
887C23—1182no—
888C23—1182no—
889C23—2361no—
890C23—2361no—
891C23—2361no—
892C23—2361no—
893C23—2361no—
894C23—2361no—
895C23—2361no—
896C23—2361no—
897C23—2361no—
898C23—2361no—
899C23—2361no—
900C23—2361no—
901C23—2361no—
902C23—2361no—
903C23—2361no—
904C23—2361no—
905C23C22⋊C4×D5911yescharacteristic
906C23#1427369511yescharacteristic
907C23#1427369511yescharacteristic
908C23#1427369711yescharacteristic
909C23#1427369811yescharacteristic
910C23#1427370011yescharacteristic
911C23#1427370911yescharacteristic
912C23D8×D5911yescharacteristic
913C23SD16×D5911yescharacteristic
914C23#1427374611yescharacteristic
915C23#1427374811yescharacteristic
916C23#1427375111yescharacteristic
917C23#1427375111yescharacteristic
918C23#1427375411yescharacteristic
919C23#1427375611yescharacteristic
920D4—24no—
921D4—24no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—23632no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—1182no—
937C2×C4—1184no—
938C2×C4—1182no—
939C2×C4—1182no—
940C2×C4—4721no—
941C2×C4—4721no—
942C2×C4—4721no—
943C2×C4—4721no—
944C2×C4—2362no—
945C2×C4—2362no—
946C2×C4—2362no—
947C2×C4—2362no—
948C2×C4—2362no—
949C2×C4—2362no—
950C2×C4—2362no—
951C2×C4—2362no—
952C2×C4—2362no—
953C2×C4—2361no—
954C2×C4—2361no—
955C2×C4—2361no—
956C2×C4—2361no—
957C2×C4—2362no—
958C2×C4—2362no—
959C2×C4—2362no—
960C2×C4—2362no—
961C2×C4—2362no—
962C2×C4—2362no—
963C2×C4—2362no—
964C2×C4—2362no—
965C2×C4C22⋊C4×D5911yescharacteristic
966C2×C4C2×(C2×D59)⋊C411yescharacteristic
967C2×C4(C22⋊D59)⋊C411yescharacteristic
968C2×C4(C22⋊D59)⋊C411yescharacteristic
969C2×C4C4×C22⋊D5911yescharacteristic
970C2×C4C4×C22⋊D5911yescharacteristic
971C2×C4#1427369511yescharacteristic
972C2×C4#1427369511yescharacteristic
973C2×C4#1427369611yescharacteristic
974C2×C4#1427369711yescharacteristic
975C2×C4#1427369711yescharacteristic
976C2×C4#1427369811yescharacteristic
977C2×C4#1427369911yescharacteristic
978C2×C4#1427369911yescharacteristic
979C2×C4#1427369911yescharacteristic
980C2×C4#1427369911yescharacteristic
981C2×C4#1427370011yescharacteristic
982C2×C4#1427370011yescharacteristic
983C2×C4#1427370011yescharacteristic
984C2×C4#1427370111yescharacteristic
985C2×C4#1427370111yescharacteristic
986C2×C4#1427370911yescharacteristic
987C2×C4#1427371011yescharacteristic
988C2×C4#1427371111yescharacteristic
989C2×C4#1427371311yescharacteristic
990C2×C4#1427371311yescharacteristic
991C2×C4#1427372311yescharacteristic
992C2×C4#1427372311yescharacteristic
993C8—42no—
994C8—2362no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—82no—
999C22—82no—
1000C22—82no—
1001C22—82no—
1002C22—82no—
1003C22—82no—
1004C22—82no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—1184no—
1011C22—1184no—
1012C22—1184no—
1013C22—2362no—
1014C22—2362no—
1015C22—2362no—
1016C22—2362no—
1017C22—2362no—
1018C22—2362no—
1019C22—2362no—
1020C22—2362no—
1021C22—2362no—
1022C22—2362no—
1023C22—2362no—
1024C22—2362no—
1025C22#1683725711yescharacteristic
1026C22#1683727811yescharacteristic
1027C22#1683727811yescharacteristic
1028C22#1683731011yescharacteristic
1029C22#1683731111yescharacteristic
1030C22#1683731711yescharacteristic
1031C22#1683731811yescharacteristic
1032C22#102×D5911yescharacteristic
1033C22#1683739511yescharacteristic
1034C22#1683740011yescharacteristic
1035C22#1683740511yescharacteristic
1036C22#1683753411yescharacteristic
1037C22#1683753411yescharacteristic
1038C22#1683753711yescharacteristic
1039C22#1683753911yescharacteristic
1040C22#1683754411yescharacteristic
1041C22#1683754411yescharacteristic
1042C22#1683754611yescharacteristic
1043C22#1683754811yescharacteristic
1044C22#1683755111yescharacteristic
1045C22#1683755411yescharacteristic
1046C22#1683756111yescharacteristic
1047C22#1683756511yescharacteristic
1048C22#1683762811yescharacteristic
1049C22#1683763011yescharacteristic
1050C22#1683763511yescharacteristic
1051C22#1683763711yescharacteristic
1052C22#1683764511yescharacteristic
1053C22#1683764711yescharacteristic
1054C22#1683765211yescharacteristic
1055C22#1683765411yescharacteristic
1056C22#1683771411yescharacteristic
1057C22#1683771911yescharacteristic
1058C22#1683772411yescharacteristic
1059C22#1683772511yescharacteristic
1060C4—82no—
1061C4—4722no—
1062C4—2364no—
1063C4—2362no—
1064C4#1683727911yescharacteristic
1065C4#1683728111yescharacteristic
1066C4#1683730211yescharacteristic
1067C4#1683730211yescharacteristic
1068C4#1683731011yescharacteristic
1069C4#1683731111yescharacteristic
1070C4#1683731711yescharacteristic
1071C4#1683731811yescharacteristic
1072C2—84no—
1073C2—2364no—
1074C2#2142233511yescharacteristic
1075C2#2142402511yescharacteristic
1076C2#2142403311yescharacteristic
1077C2#2142441011yescharacteristic
1078C2#2142441511yescharacteristic
1079C2#2142452111yescharacteristic
1080C2#2142453111yescharacteristic
1081C2#2142509111yescharacteristic
1082C2#2142509311yescharacteristic
1083C2#2142509611yescharacteristic
1084C2#2142510011yescharacteristic
1085C2#2142527611yescharacteristic
1086C2#2142527711yescharacteristic
1087C2#2142528311yescharacteristic
1088C2#2142528411yescharacteristic
subgroupG/H
centerC24D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC22×#102×C59C2
socleC24×C59C2×D4
prime radicalC22×#14273698C2
cosocleC23×C4×C59C23
hypercenterC22×#102D59
hypocenterC59#10969
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#14273648C2semidirect
3. C22×(C2×D59)⋊C8C2semidirect
4. C2×#16837259C2semidirect
5. C2×#16837165C2semidirect
6. C2×#16837164C2semidirect
7. C22×#102×C59C2semidirect
16. C2×#14273698C4semidirect
69. C22×C59⋊C8D4semidirect
85. C2×C4⋊Dic59D4semidirect
118. C22×C8×C59D4semidirect
124. C2×C4⋊C4×C59D4semidirect
184. C2×D4×C59C22⋊C4semidirect
282. C4⋊Dic59C22⋊C4semidirect
374. C22×D59#102semidirect
530. C22×#102D59semidirect
582. C59#10969semidirect
638. C22×C8C22⋊D59semidirect
660. C2×C4⋊C4C22⋊D59semidirect
736. C2×D4(C2×D59)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#142736982
C22×#142736482
C22×(C2×D59)⋊C82
C2×#168372592
C2×#168371652
C2×#168371642
C22×#102×C592
#1096959