Finite Group Databasebeta

← #28515989

Subgroups — #28515989

Order 15104.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273708C211yesmaximal, characteristic
2C2×#16837296C211yesmaximal, characteristic, complemented
3C2×#16837275C211yesmaximal, characteristic, complemented
4C2×#16837260C211yesmaximal, characteristic, complemented
5#21422362C211yesmaximal, characteristic, complemented
6#21422347C211yesmaximal, characteristic, complemented
7#21422347C211yesmaximal, characteristic, complemented
8#21422343C211yesmaximal, characteristic, complemented
9#21422339C211yesmaximal, characteristic, complemented
10#21422337C211yesmaximal, characteristic
11#21422333C211yesmaximal, characteristic, complemented
12Dic59⋊#95C211yesmaximal, characteristic, complemented
13#21422319C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#386C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C2×#14273708—24no—
18C2×#14273708—24no—
19C2×#14273708C418yescomplemented
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C22⋊Dic59C2211yescharacteristic
30C22×C22⋊Dic59C2211yescharacteristic
31C22×C22⋊Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33#16837296—24no—
34#16837275—24no—
35#16837260—24no—
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C23×D4×C59C2211yescharacteristic
51C24×C4×C59C2211yescharacteristic
52C22×C22⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C59×#386—24no—
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C23×Dic59—22no—
59C23×Dic59—22no—
60C23×Dic59—22no—
61C23×Dic59—22no—
62C23×Dic59—41no—
63C23×Dic59—41no—
64C23×Dic59C2×C414yescomplemented
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73#14273708—232no—
74C2×Dic59⋊C4—22no—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—22no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4—22no—
80C2×Dic59⋊C4—22no—
81C2×Dic59⋊C4—22no—
82C2×Dic59⋊C4—22no—
83C2×Dic59⋊C4—22no—
84C2×Dic59⋊C4—41no—
85C2×Dic59⋊C4—41no—
86C2×Dic59⋊C4—41no—
87C2×Dic59⋊C4C2×C414yescomplemented
88C2×Dic59⋊C4C2×C414yescomplemented
89C2×C22⋊Dic59—22no—
90C2×C22⋊Dic59—22no—
91C2×C22⋊Dic59—22no—
92C2×C22⋊Dic59—22no—
93C2×C22⋊Dic59—22no—
94C2×C22⋊Dic59—22no—
95C2×C22⋊Dic59—22no—
96C2×C22⋊Dic59—22no—
97C2×C22⋊Dic59—22no—
98C2×C22⋊Dic59—22no—
99C2×C22⋊Dic59—41no—
100C2×C22⋊Dic59—41no—
101C2×C22⋊Dic59—41no—
102C2×C22⋊Dic59—41no—
103C2×C22⋊Dic59—41no—
104C2×C22⋊Dic59—41no—
105C2×C22⋊Dic59C2×C414yes—
106C2×C22⋊Dic59C2×C414yes—
107C2×C22⋊Dic59C2×C414yescomplemented
108C2×C22⋊Dic59D414yes—
109C2×C22⋊Dic59D414yes—
110C2×C4×Dic59—22no—
111C2×C4×Dic59—22no—
112C2×C4×Dic59—41no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—22no—
119C59⋊#95—41no—
120C59⋊#95—41no—
121C59⋊#95—41no—
122C59⋊#95—41no—
123C59⋊#95—41no—
124C59⋊#95—41no—
125C59⋊#95—41no—
126C59⋊#95—41no—
127C25×C59C2311yescharacteristic
128C25×C59C2311yescharacteristic
129C22×D4×C59—22no—
130C22×D4×C59—22no—
131C22×D4×C59—22no—
132C22×D4×C59—22no—
133C22×D4×C59—41no—
134C22×D4×C59—41no—
135C22×D4×C59C2×C414yes—
136C23×C4×C59—22no—
137C23×C4×C59—22no—
138C23×C4×C59—22no—
139C23×C4×C59—41no—
140C23×C4×C59—41no—
141C23×C4×C59—41no—
142C23×C4×C59—41no—
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C2×C22⋊C4×C59—22no—
149C2×C22⋊C4×C59—22no—
150C2×C22⋊C4×C59—22no—
151C2×C22⋊C4×C59—22no—
152C2×C22⋊C4×C59—41no—
153C2×C22⋊C4×C59—41no—
154C2×C22⋊C4×C59—41no—
155C2×C22⋊C4×C59—41no—
156C2×C22⋊C4×C59D414yes—
157#95×C59—22no—
158#95×C59—22no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—21no—
172C24×C59—21no—
173C24×C59—21no—
174C24×C59—21no—
175C24×C59—21no—
176C24×C59—21no—
177C24×C59—21no—
178C24×C59—21no—
179C24×C59—21no—
180C24×C59—21no—
181C24×C59—21no—
182C24×C59—21no—
183C24×C59C22×C412yes—
184C24×C59C22×C412yes—
185C24×C59C2×D412yes—
186C24×C59C2×D412yes—
187C24×C59C2×D412yes—
188C24×C59#4112yes—
189C24×C59C2411yescharacteristic
190C2×D4×C59—28no—
191C2×D4×C59—28no—
192C2×D4×C59—44no—
193C2×D4×C59—44no—
194C2×D4×C59—44no—
195C2×D4×C59—44no—
196C2×D4×C59—44no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—21no—
228C22×C4×C59—44no—
229C22×C4×C59—44no—
230C22×C4×C59—44no—
231C22×C4×C59—44no—
232C22×C4×C59—44no—
233C22×C4×C59—44no—
234C22×C4×C59—44no—
235C22×C4×C59C22×C412yes—
236C22×C4×C59C2×D412yes—
237C22×C4×C59C2×D412yes—
238C22×C4×C59#4112yes—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—28no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59—28no—
267C22×Dic59—21no—
268C22×Dic59—21no—
269C22×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—21no—
278C22×Dic59—21no—
279C22×Dic59—21no—
280C22×Dic59—21no—
281C22×Dic59—21no—
282C22×Dic59—21no—
283C22×Dic59—21no—
284C22×Dic59—21no—
285C22×Dic59—21no—
286C22×Dic59—21no—
287C22×Dic59—21no—
288C22×Dic59—44no—
289C22×Dic59—44no—
290C22×Dic59—44no—
291C22×Dic59—44no—
292C22×Dic59—44no—
293C22×Dic59C22×C412yes—
294C22×Dic59C22×C412yes—
295C22×Dic59C22×C412yes—
296C22×Dic59C22×C412yes—
297C22×Dic59C2×D412yes—
298C22×Dic59C2×D412yes—
299C22×Dic59C2×D412yes—
300C22×Dic59C2×D412yes—
301C22×Dic59#4112yes—
302C22⋊C4×C59—44no—
303C22⋊C4×C59—44no—
304C22⋊C4×C59—44no—
305C22⋊Dic59—28no—
306C22⋊Dic59—28no—
307C22⋊Dic59—44no—
308C22⋊Dic59—44no—
309C22⋊Dic59—44no—
310C22⋊Dic59—44no—
311C22⋊Dic59C22⋊C4116yescomplemented
312Dic59⋊C4—28no—
313Dic59⋊C4—28no—
314Dic59⋊C4—44no—
315Dic59⋊C4—44no—
316Dic59⋊C4—44no—
317C4×Dic59—44no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—22no—
325C23×C59—22no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—22no—
333C23×C59—22no—
334C23×C59—22no—
335C23×C59—22no—
336C23×C59—22no—
337C23×C59—22no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—22no—
343C23×C59—22no—
344C23×C59—22no—
345C23×C59—22no—
346C23×C59—22no—
347C23×C59—22no—
348C23×C59—22no—
349C23×C59—22no—
350C23×C59—22no—
351C23×C59—22no—
352C23×C59—22no—
353C23×C59—22no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—41no—
360C23×C59—41no—
361C23×C59—41no—
362C23×C59—41no—
363C23×C59—41no—
364C23×C59—41no—
365C23×C59—41no—
366C23×C59—41no—
367C23×C59—41no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—41no—
377C23×C59—41no—
378C23×C59—41no—
379C23×C59—41no—
380C23×C59—41no—
381C23×C59—41no—
382C23×C59—41no—
383C23×C59—41no—
384C23×C59—41no—
385C23×C59—41no—
386C23×C59C2×C22⋊C414yes—
387C23×C59C4×D414yes—
388C23×C59C23×C411yescharacteristic
389C23×C59C22×D411yescharacteristic
390C23×C59C22×D411yescharacteristic
391C23×C59C22×D411yescharacteristic
392C23×C59C2×#4111yescharacteristic
393C23×C59C2×#4111yescharacteristic
394C23×C59C2×#4111yescharacteristic
395C23×C59H(5,𝔽2)11yescharacteristic
396C23×C59H(5,𝔽2)11yescharacteristic
397C23×C59H(5,𝔽2)11yescharacteristic
398C23×C59H(5,𝔽2)11yescharacteristic
399C23×C59H(5,𝔽2)11yescharacteristic
400C23×C592−1+411yescharacteristic
401C23×C592−1+411yescharacteristic
402C23×C592−1+411yescharacteristic
403D4×C59—416no—
404C2×C4×C59—22no—
405C2×C4×C59—22no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—416no—
417C2×C4×C59—41no—
418C2×C4×C59—41no—
419C2×C4×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—41no—
440C2×Dic59—22no—
441C2×Dic59—22no—
442C2×Dic59—22no—
443C2×Dic59—22no—
444C2×Dic59—22no—
445C2×Dic59—22no—
446C2×Dic59—22no—
447C2×Dic59—22no—
448C2×Dic59—22no—
449C2×Dic59—22no—
450C2×Dic59—22no—
451C2×Dic59—22no—
452C2×Dic59—22no—
453C2×Dic59—22no—
454C2×Dic59—22no—
455C2×Dic59—22no—
456C2×Dic59—22no—
457C2×Dic59—22no—
458C2×Dic59—22no—
459C2×Dic59—22no—
460C2×Dic59—22no—
461C2×Dic59—416no—
462C2×Dic59—41no—
463C2×Dic59—41no—
464C2×Dic59—41no—
465C2×Dic59—41no—
466C2×Dic59—41no—
467C2×Dic59—41no—
468C2×Dic59—41no—
469C2×Dic59—41no—
470C2×Dic59—41no—
471C2×Dic59—41no—
472C2×Dic59—41no—
473C2×Dic59—41no—
474C2×Dic59—41no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477C2×Dic59—41no—
478C2×Dic59—41no—
479C2×Dic59—41no—
480C2×Dic59—41no—
481C2×Dic59—41no—
482C2×Dic59—41no—
483C2×Dic59—41no—
484C2×Dic59—41no—
485C2×Dic59—41no—
486C2×Dic59—41no—
487C2×Dic59—41no—
488C2×Dic59—41no—
489C2×Dic59—41no—
490C2×Dic59—41no—
491C2×Dic59—41no—
492C2×Dic59—41no—
493C2×Dic59—41no—
494C2×Dic59—41no—
495C2×Dic59C2×C22⋊C414yes—
496C2×Dic59C2×C22⋊C414yes—
497#14359—591nomaximal, Sylow
498C22×C59—24no—
499C22×C59—24no—
500C22×C59—24no—
501C22×C59—24no—
502C22×C59—24no—
503C22×C59—24no—
504C22×C59—42no—
505C22×C59—42no—
506C22×C59—42no—
507C22×C59—42no—
508C22×C59—42no—
509C22×C59—42no—
510C22×C59—42no—
511C22×C59—42no—
512C22×C59—42no—
513C22×C59—42no—
514C22×C59—42no—
515C22×C59—42no—
516C22×C59—42no—
517C22×C59—42no—
518C22×C59—42no—
519C22×C59—42no—
520C22×C59—42no—
521C22×C59—42no—
522C22×C59—42no—
523C22×C59—42no—
524C22×C59—42no—
525C22×C59—42no—
526C22×C59—42no—
527C22×C59—42no—
528C22×C59C22×C22⋊C411yescharacteristic
529C22×C59C2×C4×D411yescharacteristic
530C22×C59C4×#4111yescharacteristic
531C22×C59#51811yescharacteristic
532C22×C59#52011yescharacteristic
533C22×C59#52011yescharacteristic
534C22×C59#52011yescharacteristic
535C22×C59#53411yescharacteristic
536C22×C59#53511yescharacteristic
537C22×C59#53611yescharacteristic
538C22×C59#53611yescharacteristic
539C22×C59#53711yescharacteristic
540C22×C59#53711yescharacteristic
541C22×C59#53811yescharacteristic
542C22×C59#53911yescharacteristic
543C22×C59#53911yescharacteristic
544C22×C59#53911yescharacteristic
545C22×C59#54011yescharacteristic
546C22×C59#54211yescharacteristic
547C22×C59D4211yescharacteristic
548C22×C59D4211yescharacteristic
549C22×C59#54611yescharacteristic
550C22×C59#54611yescharacteristic
551C22×C59#54611yescharacteristic
552C22×C59#54611yescharacteristic
553C22×C59#54611yescharacteristic
554C22×C59#54711yescharacteristic
555C22×C59#54711yescharacteristic
556C22×C59#54711yescharacteristic
557C22×C59#55111yescharacteristic
558C22×C59#55211yescharacteristic
559C22×C59#56011yescharacteristic
560C22×C59#56211yescharacteristic
561C22×C59#56211yescharacteristic
562C22×C59#56311yescharacteristic
563C4×C59—42no—
564C4×C59—42no—
565C4×C59—42no—
566C4×C59—42no—
567C4×C59—81no—
568Dic59—24no—
569Dic59—24no—
570Dic59—42no—
571Dic59—42no—
572Dic59—42no—
573Dic59—81no—
574Dic59—81no—
575Dic59—81no—
576C22×#123—591no—
577C2×#388—591no—
578C2×#386D5911yescharacteristic
579C2×#385—591no—
580C2×#380—591no—
581#1445—591no—
582#1441—591no—
583#1441—591no—
584#1440—591no—
585#1439—591no—
586#1438—591no—
587#1437—591no—
588C4⋊#95—591no—
589C22⋊#95—591no—
590C22⋊#95—591no—
591C2×C59—44no—
592C2×C59—44no—
593C2×C59#231111yescharacteristic
594C2×C59#232211yescharacteristic
595C2×C59#233511yescharacteristic
596C2×C59D4×C22⋊C411yescharacteristic
597C2×C59#233911yescharacteristic
598C2×C59#235911yescharacteristic
599C2×C59#237611yescharacteristic
600C2×C59#267111yescharacteristic
601C2×C59#267211yescharacteristic
602C2×C59#267811yescharacteristic
603C2×C59#268011yescharacteristic
604C2×C59#268711yescharacteristic
605C2×C59#269311yescharacteristic
606C2×C59#269511yescharacteristic
607C2×C59#270611yescharacteristic
608C23×D4C2×D5911yescharacteristic
609C24×C4—591no—
610C24×C4C2×D5911yescharacteristic
611C2×#123—598no—
612C2×#123—1184no—
613C2×#123—1184no—
614C22×C4⋊C4—591no—
615C22×C4⋊C4—591no—
616C22×C4⋊C4—591no—
617C22×C4⋊C4—591no—
618C22×C4⋊C4—591no—
619C22×C22⋊C4—591no—
620C22×C22⋊C4—591no—
621C22×C22⋊C4—591no—
622C22×C22⋊C4—591no—
623C22×C22⋊C4—591no—
624C22×C22⋊C4—591no—
625C22×C22⋊C4—591no—
626C22×C22⋊C4C2×D5911yescharacteristic
627C22×C22⋊C4C2×D5911yescharacteristic
628C22×C22⋊C4C2×D5911yescharacteristic
629C22×C42—591no—
630#388—1184no—
631#386—24no—
632#385—1184no—
633#380—1184no—
634C2×#95—591no—
635C2×#95—591no—
636C2×#95—591no—
637C2×#95—591no—
638C2×#95—591no—
639C2×#95—591no—
640C2×#95—591no—
641C2×#95—591no—
642C2×#95—591no—
643C2×#95—591no—
644C2×#95—591no—
645C2×#95—591no—
646C2×#95—591no—
647C2×#95—591no—
648C2×#95C2×D5911yescharacteristic
649C2×#95C2×D5911yescharacteristic
650C59#1435911yescharacteristic, complemented, Sylow
651C25C22×D5911yescharacteristic
652C25C22×D5911yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C4×D5914yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4—41no—
666C23×C4—41no—
667C23×C4—591no—
668C23×C4—591no—
669C23×C4—591no—
670C23×C4—591no—
671C23×C4—591no—
672C23×C4—594no—
673C23×C4—591no—
674C23×C4—591no—
675C23×C4—591no—
676C23×C4—1182no—
677C23×C4—1182no—
678C23×C4—1182no—
679C23×C4—1182no—
680C23×C4—2361no—
681C23×C4—2361no—
682C23×C4C22×D5911yescharacteristic
683C23×C4C22×D5911yescharacteristic
684C23×C4C22×D5911yescharacteristic
685C23×C4C22×D5911yescharacteristic
686C23×C4C22×D5911yescharacteristic
687#123—11832no—
688C2×C4⋊C4—594no—
689C2×C4⋊C4—594no—
690C2×C4⋊C4—1182no—
691C2×C4⋊C4—1182no—
692C2×C4⋊C4—1182no—
693C2×C4⋊C4—1182no—
694C2×C4⋊C4—1182no—
695C2×C4⋊C4—1182no—
696C2×C4⋊C4—1182no—
697C2×C4⋊C4—1182no—
698C2×C4⋊C4—1182no—
699C2×C4⋊C4—1182no—
700C2×C4⋊C4—2361no—
701C2×C4⋊C4—2361no—
702C2×C4⋊C4—2361no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—594no—
712C2×C22⋊C4—594no—
713C2×C22⋊C4—594no—
714C2×C22⋊C4—594no—
715C2×C22⋊C4—594no—
716C2×C22⋊C4—1182no—
717C2×C22⋊C4—1182no—
718C2×C22⋊C4—1182no—
719C2×C22⋊C4—1182no—
720C2×C22⋊C4—1182no—
721C2×C22⋊C4—1182no—
722C2×C22⋊C4—1182no—
723C2×C22⋊C4—1182no—
724C2×C22⋊C4—1182no—
725C2×C22⋊C4—1182no—
726C2×C22⋊C4—2361no—
727C2×C22⋊C4—2361no—
728C2×C22⋊C4—2361no—
729C2×C22⋊C4—2361no—
730C2×C22⋊C4—2361no—
731C2×C22⋊C4—2361no—
732C2×C22⋊C4C22⋊D5914yes—
733C2×C42—1182no—
734C2×C42—1182no—
735C2×C42—2361no—
736#95—22no—
737#95—22no—
738#95—1182no—
739#95—1182no—
740#95—1182no—
741#95—1182no—
742#95—1182no—
743#95—1182no—
744#95—2361no—
745#95—2361no—
746#95—2361no—
747#95—2361no—
748#95—2361no—
749#95—2361no—
750#95—2361no—
751#95—2361no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C2×C4×D5912yes—
777C24C2×C4×D5912yes—
778C24#1174568512yes—
779C24D4×D5912yes—
780C24D4×D5912yes—
781C24C2×C22⋊D5912yes—
782C24C23×D5911yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—592no—
829C22×C4—592no—
830C22×C4—592no—
831C22×C4—592no—
832C22×C4—592no—
833C22×C4—592no—
834C22×C4—592no—
835C22×C4—592no—
836C22×C4—592no—
837C22×C4—1188no—
838C22×C4—1181no—
839C22×C4—1181no—
840C22×C4—1181no—
841C22×C4—1181no—
842C22×C4—1181no—
843C22×C4—1181no—
844C22×C4—1181no—
845C22×C4—1181no—
846C22×C4—1188no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—1181no—
855C22×C4—1181no—
856C22×C4—1181no—
857C22×C4—1181no—
858C22×C4—1181no—
859C22×C4—1181no—
860C22×C4—1181no—
861C22×C4—1181no—
862C22×C4—1181no—
863C22×C4—1181no—
864C22×C4—1181no—
865C22×C4—1181no—
866C22×C4—1181no—
867C22×C4—1181no—
868C22×C4—1181no—
869C22×C4—1181no—
870C22×C4—1181no—
871C22×C4—1181no—
872C22×C4—1181no—
873C22×C4—1181no—
874C22×C4—1181no—
875C22×C4—1181no—
876C22×C4—1181no—
877C22×C4—1181no—
878C22×C4—1181no—
879C22×C4—1181no—
880C22×C4—1181no—
881C22×C4—1181no—
882C22×C4—1181no—
883C22×C4—1181no—
884C22×C4—1181no—
885C22×C4—1181no—
886C22×C4—2364no—
887C22×C4—2364no—
888C22×C4—2364no—
889C22×C4—2364no—
890C22×C4—2364no—
891C22×C4C2×C4×D5912yes—
892C22×C4#1174568712yes—
893C22×C4C2×C22⋊D5912yes—
894C22×C4C2×C22⋊D5912yes—
895C4⋊C4—1188no—
896C4⋊C4—1188no—
897C4⋊C4—2364no—
898C4⋊C4—2364no—
899C4⋊C4—2364no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—5916no—
904C22⋊C4—1188no—
905C22⋊C4—1188no—
906C22⋊C4—2364no—
907C22⋊C4—2364no—
908C22⋊C4—2364no—
909C22⋊C4—2364no—
910C42—2364no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C22⋊C4×D5914yes—
980C23C4×C22⋊D5914yes—
981C23C22×C4×D5911yescharacteristic
982C23C2×D4×D5911yescharacteristic
983C23C2×D4×D5911yescharacteristic
984C23C22×C22⋊D5911yescharacteristic
985C23#41×D5911yescharacteristic
986C23C2×#1174568711yescharacteristic
987C23C2×#1174568511yescharacteristic
988C23#1427377211yescharacteristic
989C23#1427377211yescharacteristic
990C23#1427377211yescharacteristic
991C23#1427377211yescharacteristic
992C23#1427377211yescharacteristic
993C23#1427377411yescharacteristic
994C23#1427377411yescharacteristic
995C23#1427377411yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—416no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—594no—
1034C2×C4—594no—
1035C2×C4—1182no—
1036C2×C4—1182no—
1037C2×C4—1182no—
1038C2×C4—1182no—
1039C2×C4—1182no—
1040C2×C4—1182no—
1041C2×C4—1182no—
1042C2×C4—1182no—
1043C2×C4—1182no—
1044C2×C4—1182no—
1045C2×C4—1182no—
1046C2×C4—1182no—
1047C2×C4—1182no—
1048C2×C4—1182no—
1049C2×C4—1182no—
1050C2×C4—1182no—
1051C2×C4—1182no—
1052C2×C4—1182no—
1053C2×C4—1182no—
1054C2×C4—1182no—
1055C2×C4—1182no—
1056C2×C4—23616no—
1057C2×C4—2361no—
1058C2×C4—2361no—
1059C2×C4—2361no—
1060C2×C4—2361no—
1061C2×C4—2361no—
1062C2×C4—2361no—
1063C2×C4—2361no—
1064C2×C4—2361no—
1065C2×C4—2361no—
1066C2×C4—2361no—
1067C2×C4—2361no—
1068C2×C4—2361no—
1069C2×C4—2361no—
1070C2×C4—2361no—
1071C2×C4—2361no—
1072C2×C4—2361no—
1073C2×C4—2361no—
1074C2×C4—2361no—
1075C2×C4—2361no—
1076C2×C4—2361no—
1077C2×C4—2361no—
1078C2×C4—2361no—
1079C2×C4—2361no—
1080C2×C4—2361no—
1081C2×C4—2361no—
1082C2×C4—2361no—
1083C2×C4—2361no—
1084C2×C4—2361no—
1085C2×C4—2361no—
1086C2×C4—2361no—
1087C2×C4—2361no—
1088C2×C4—2361no—
1089C2×C4—2361no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C2×C22⋊C4×D5911yescharacteristic
1121C22C2×C4×C22⋊D5911yescharacteristic
1122C22C4×#1174568711yescharacteristic
1123C22#1683787511yescharacteristic
1124C22#1683788111yescharacteristic
1125C22#1683788111yescharacteristic
1126C22#1683788111yescharacteristic
1127C22#1683796111yescharacteristic
1128C22#1683796711yescharacteristic
1129C22#1683797311yescharacteristic
1130C22#1683797411yescharacteristic
1131C22#1683797911yescharacteristic
1132C22#1683797911yescharacteristic
1133C22#1683798711yescharacteristic
1134C22#1683799411yescharacteristic
1135C22#1683799411yescharacteristic
1136C22#1683799511yescharacteristic
1137C22#1683800211yescharacteristic
1138C22#1683801911yescharacteristic
1139C22D4×C22⋊D5911yescharacteristic
1140C22D4×C22⋊D5911yescharacteristic
1141C22#1683803911yescharacteristic
1142C22#1683804111yescharacteristic
1143C22#1683804211yescharacteristic
1144C22#1683804211yescharacteristic
1145C22#1683804611yescharacteristic
1146C22#1683805011yescharacteristic
1147C22#1683805111yescharacteristic
1148C22#1683805211yescharacteristic
1149C22#1683808111yescharacteristic
1150C22#1683809211yescharacteristic
1151C22#1683814111yescharacteristic
1152C22#1683814711yescharacteristic
1153C22#1683814711yescharacteristic
1154C22#1683815511yescharacteristic
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—1184no—
1161C4—1184no—
1162C4—4721no—
1163C4—4721no—
1164C4—4721no—
1165C4—2362no—
1166C4—2362no—
1167C4—2362no—
1168C2—44no—
1169C2—44no—
1170C2#2142668311yescharacteristic
1171C2#2142676111yescharacteristic
1172C2#2142688711yescharacteristic
1173C2C22⋊C4×C22⋊D5911yescharacteristic
1174C2#2142692211yescharacteristic
1175C2#2142708211yescharacteristic
1176C2#2142723911yescharacteristic
1177C2#2143032611yescharacteristic
1178C2#2143034111yescharacteristic
1179C2#2143042111yescharacteristic
1180C2#2143043311yescharacteristic
1181C2#2143052111yescharacteristic
1182C2#2143060211yescharacteristic
1183C2#2143062611yescharacteristic
1184C2#2143078711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#386C2
socle, cosocleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC2×#386D59
hypocenterC59#14359
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#16837296C2semidirect
3. C2×#16837275C2semidirect
4. C2×#16837260C2semidirect
5. #21422362C2semidirect
6. #21422347C2semidirect
7. #21422347C2semidirect
8. #21422343C2semidirect
9. #21422339C2semidirect
11. #21422333C2semidirect
12. Dic59⋊#95C2semidirect
13. #21422319C2semidirect
14. #21422318C2semidirect
19. C2×#14273708C4semidirect
64. C23×Dic59C2×C4semidirect
87. C2×Dic59⋊C4C2×C4semidirect
88. C2×Dic59⋊C4C2×C4semidirect
107. C2×C22⋊Dic59C2×C4semidirect
311. C22⋊Dic59C22⋊C4semidirect
650. C59#14359semidirect

Maximal subgroups

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

subgroupindex
C22×#142737082
C2×#168372962
C2×#168372752
C2×#168372602
#214223622
#214223472
#214223432
#214223392
#214223372
#214223332
Dic59⋊#952
#214223192
#214223182
C2×C59×#3862
#1435959