Finite Group Databasebeta

← #28510819

Subgroups — #28510819

Order 15104.

2546 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic59C211yesmaximal, characteristic
2C2×#16837282C211yesmaximal, characteristic
3C2×#16837263C211yesmaximal, characteristic, complemented
4C22×C59⋊#95C211yesmaximal, characteristic, complemented
5#21422365C211yesmaximal, characteristic, complemented
6#21422363C211yesmaximal, characteristic, complemented
7#21422343C211yesmaximal, characteristic, complemented
8#21422343C211yesmaximal, characteristic, complemented
9#21422320C211yesmaximal, characteristic, complemented
10#21422320C211yesmaximal, characteristic, complemented
11#21422319C211yesmaximal, characteristic, complemented
12#21422318C211yesmaximal, characteristic, complemented
13#21422318C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#386C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C24×Dic59C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C2×D4×Dic59—24no—
20C2×D4×Dic59—24no—
21C2×D4×Dic59C418yescomplemented
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C4×Dic59C2211yescharacteristic
29#16837282—24no—
30#16837263—24no—
31C2×C59⋊#95—24no—
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2211yescharacteristic
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
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—22no—
63C23×Dic59—22no—
64C23×Dic59—22no—
65C23×Dic59—22no—
66C23×Dic59—22no—
67C23×Dic59—22no—
68C23×Dic59—22no—
69C23×Dic59—22no—
70C23×Dic59—22no—
71C23×Dic59—41no—
72C23×Dic59—41no—
73C23×Dic59—41no—
74C23×Dic59—41no—
75C23×Dic59—41no—
76C23×Dic59—41no—
77C23×Dic59C2×C414yes—
78C23×Dic59C2×C414yescomplemented
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85C23×Dic59C2311yescharacteristic
86C23×Dic59C2311yescharacteristic
87D4×Dic59—232no—
88C2×C4⋊Dic59—22no—
89C2×C4⋊Dic59—22no—
90C2×C4⋊Dic59C2×C414yescomplemented
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—22no—
100C2×C22⋊Dic59—22no—
101C2×C22⋊Dic59—22no—
102C2×C22⋊Dic59—41no—
103C2×C22⋊Dic59—41no—
104C2×C22⋊Dic59C2×C414yes—
105C2×C22⋊Dic59C2×C414yescomplemented
106C2×C4×Dic59—22no—
107C2×C4×Dic59—22no—
108C2×C4×Dic59C2×C414yescomplemented
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—22no—
119C59⋊#95—22no—
120C59⋊#95—41no—
121C59⋊#95—41no—
122C59⋊#95—41no—
123C59⋊#95—41no—
124C59⋊#95—41no—
125C59⋊#95—41no—
126C59⋊#95D414yescomplemented
127C25×C59C2311yescharacteristic
128C25×C59C2311yescharacteristic
129C22×D4×C59—22no—
130C22×D4×C59—22no—
131C22×D4×C59—22no—
132C22×D4×C59—22no—
133C22×D4×C59C2×C414yes—
134C22×D4×C59D414yes—
135C22×D4×C59D414yes—
136C23×C4×C59—22no—
137C23×C4×C59—22no—
138C23×C4×C59—22no—
139C23×C4×C59—22no—
140C23×C4×C59—22no—
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—22no—
153C2×C22⋊C4×C59—22no—
154C2×C22⋊C4×C59—22no—
155C2×C22⋊C4×C59—41no—
156C2×C22⋊C4×C59—41no—
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×C59C22×C412yes—
180C24×C59C22×C412yes—
181C24×C59C2×D412yes—
182C24×C59C2×D412yes—
183C24×C59C2×D412yes—
184C24×C59C2×D412yes—
185C24×C59#4112yes—
186C24×C59#4112yes—
187C24×C59#4112yes—
188C24×C59#4112yes—
189C24×C59C2411yescharacteristic
190C2×D4×C59—28no—
191C2×D4×C59—28no—
192C2×D4×C59—28no—
193C2×D4×C59—28no—
194C2×D4×C59—28no—
195C2×D4×C59—28no—
196C2×D4×C59C22⋊C4116yes—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—28no—
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×C59C22×C412yes—
235C22×C4×C59C2×D412yes—
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—28no—
244C22×Dic59—28no—
245C22×Dic59—28no—
246C22×Dic59—21no—
247C22×Dic59—21no—
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—21no—
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—28no—
277C22×Dic59—28no—
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—21no—
289C22×Dic59—21no—
290C22×Dic59—21no—
291C22×Dic59—21no—
292C22×Dic59—44no—
293C22×Dic59—44no—
294C22×Dic59—44no—
295C22×Dic59—44no—
296C22×Dic59—44no—
297C22×Dic59—44no—
298C22×Dic59—44no—
299C22×Dic59—44no—
300C22×Dic59—44no—
301C22×Dic59—44no—
302C22×Dic59—44no—
303C22×Dic59—44no—
304C22×Dic59—44no—
305C22×Dic59—44no—
306C22×Dic59—44no—
307C22×Dic59—44no—
308C22×Dic59C22×C412yes—
309C22×Dic59C22×C412yes—
310C22×Dic59C22×C412yes—
311C22×Dic59C22×C412yes—
312C22×Dic59C2×D412yes—
313C22×Dic59C2×D412yes—
314C22×Dic59#4112yes—
315C22×Dic59#4112yes—
316C22⋊C4×C59—44no—
317C22⋊C4×C59—44no—
318C22⋊C4×C59—44no—
319C22⋊Dic59—28no—
320C22⋊Dic59—28no—
321C22⋊Dic59—44no—
322C22⋊Dic59—44no—
323C22⋊Dic59—44no—
324C4⋊Dic59—28no—
325C4×Dic59—28no—
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—22no—
355C23×C59—22no—
356C23×C59—22no—
357C23×C59—22no—
358C23×C59—22no—
359C23×C59—22no—
360C23×C59—22no—
361C23×C59—22no—
362C23×C59—22no—
363C23×C59—22no—
364C23×C59—22no—
365C23×C59—22no—
366C23×C59—22no—
367C23×C59—22no—
368C23×C59—22no—
369C23×C59—22no—
370C23×C59—22no—
371C23×C59—22no—
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×C59—41no—
387C23×C59—41no—
388C23×C59C2×C22⋊C414yes—
389C23×C59C2×C22⋊C414yes—
390C23×C59#11714yes—
391C23×C59#11714yes—
392C23×C59#12314yes—
393C23×C59#12314yes—
394C23×C59#12314yes—
395C23×C59#12314yes—
396C23×C59C23×C411yescharacteristic
397C23×C59C22×D411yescharacteristic
398C23×C59C22×D411yescharacteristic
399C23×C59C22×D411yescharacteristic
400C23×C59C2×#4111yescharacteristic
401C23×C59C2×#4111yescharacteristic
402C23×C59C2×#4111yescharacteristic
403C23×C59C2×#4111yescharacteristic
404C23×C59C2×#4111yescharacteristic
405C23×C59C2×#4111yescharacteristic
406C23×C59C2×#4111yescharacteristic
407C23×C59H(5,𝔽2)11yescharacteristic
408C23×C59H(5,𝔽2)11yescharacteristic
409C23×C59H(5,𝔽2)11yescharacteristic
410C23×C592−1+411yescharacteristic
411D4×C59—232no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—416no—
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×C4×C59—41no—
441C2×C4×C59—41no—
442C2×C4×C59—41no—
443C2×C4×C59—41no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
446C2×C4×C59—41no—
447C2×C4×C59C2×C22⋊C414yes—
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—22no—
462C2×Dic59—22no—
463C2×Dic59—22no—
464C2×Dic59—22no—
465C2×Dic59—22no—
466C2×Dic59—22no—
467C2×Dic59—22no—
468C2×Dic59—22no—
469C2×Dic59—416no—
470C2×Dic59—416no—
471C2×Dic59—416no—
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×Dic59—41no—
496C2×Dic59—41no—
497C2×Dic59—41no—
498C2×Dic59—41no—
499C2×Dic59—41no—
500C2×Dic59—41no—
501C2×Dic59—41no—
502C2×Dic59—41no—
503C2×Dic59—41no—
504C2×Dic59—41no—
505C2×Dic59—41no—
506C2×Dic59C4×D414yes—
507#13894—591nomaximal, Sylow
508C22×C59—24no—
509C22×C59—24no—
510C22×C59—24no—
511C22×C59—24no—
512C22×C59—24no—
513C22×C59—24no—
514C22×C59—24no—
515C22×C59—24no—
516C22×C59—24no—
517C22×C59—24no—
518C22×C59—24no—
519C22×C59—24no—
520C22×C59—24no—
521C22×C59—24no—
522C22×C59—24no—
523C22×C59—24no—
524C22×C59—24no—
525C22×C59—42no—
526C22×C59—42no—
527C22×C59—42no—
528C22×C59—42no—
529C22×C59—42no—
530C22×C59—42no—
531C22×C59—42no—
532C22×C59—42no—
533C22×C59—42no—
534C22×C59—42no—
535C22×C59—42no—
536C22×C59—42no—
537C22×C59#38118yescomplemented
538C22×C59C22×C22⋊C411yescharacteristic
539C22×C59C2×#11711yescharacteristic
540C22×C59C2×#11711yescharacteristic
541C22×C59C2×C4×D411yescharacteristic
542C22×C59C4×#4111yescharacteristic
543C22×C59#51811yescharacteristic
544C22×C59#52011yescharacteristic
545C22×C59C2×#12311yescharacteristic
546C22×C59C2×#12311yescharacteristic
547C22×C59C2×#12311yescharacteristic
548C22×C59C2×#12311yescharacteristic
549C22×C59#52511yescharacteristic
550C22×C59#52511yescharacteristic
551C22×C59#52911yescharacteristic
552C22×C59#52911yescharacteristic
553C22×C59#53811yescharacteristic
554C22×C59#53811yescharacteristic
555C22×C59#53911yescharacteristic
556C22×C59#53911yescharacteristic
557C22×C59D4211yescharacteristic
558C22×C59D4211yescharacteristic
559C22×C59#54611yescharacteristic
560C22×C59#54611yescharacteristic
561C22×C59#54611yescharacteristic
562C22×C59#54611yescharacteristic
563C22×C59#54611yescharacteristic
564C22×C59#54711yescharacteristic
565C22×C59#54711yescharacteristic
566C22×C59#54811yescharacteristic
567C22×C59#55111yescharacteristic
568C22×C59#55111yescharacteristic
569C22×C59#55211yescharacteristic
570C22×C59#55311yescharacteristic
571C22×C59#55311yescharacteristic
572C22×C59#55311yescharacteristic
573C4×C59—24no—
574C4×C59—42no—
575C4×C59—42no—
576C4×C59—81no—
577C4×C59—81no—
578Dic59—24no—
579Dic59—42no—
580Dic59—42no—
581Dic59—42no—
582Dic59—42no—
583Dic59—42no—
584Dic59—81no—
585Dic59—81no—
586C22×C4×D4—591no—
587C2×#386—591no—
588C2×#386D5911yescharacteristic
589C2×#381—591no—
590C22×#95—591no—
591#1445—591no—
592#1445—591no—
593#1440—591no—
594#1440—591no—
595#1434—591no—
596#1434—591no—
597C22⋊#95—591no—
598C22⋊#95—591no—
599C22⋊#95—591no—
600C22⋊#95—591no—
601C2×C59—28no—
602C2×C59—44no—
603C2×C59C2×#38111yescharacteristic
604C2×C59#229011yescharacteristic
605C2×C59#231811yescharacteristic
606C2×C59D4×C22⋊C411yescharacteristic
607C2×C59#233911yescharacteristic
608C2×C59#235211yescharacteristic
609C2×C59#235311yescharacteristic
610C2×C59#241811yescharacteristic
611C2×C59#241811yescharacteristic
612C2×C59#241911yescharacteristic
613C2×C59#241911yescharacteristic
614C2×C59#244311yescharacteristic
615C2×C59#244311yescharacteristic
616C2×C59#244411yescharacteristic
617C2×C59#244411yescharacteristic
618C23×D4C2×D5911yescharacteristic
619C24×C4—591no—
620C24×C4—591no—
621C24×C4—591no—
622C24×C4C2×D5911yescharacteristic
623C2×C4×D4—598no—
624C2×C4×D4—1184no—
625C2×C4×D4—1184no—
626C22×C4⋊C4—591no—
627C22×C22⋊C4—591no—
628C22×C22⋊C4—591no—
629C22×C22⋊C4—591no—
630C22×C22⋊C4—591no—
631C22×C22⋊C4—591no—
632C22×C22⋊C4C2×D5911yescharacteristic
633C22×C22⋊C4C2×D5911yescharacteristic
634C22×C22⋊C4C2×D5911yescharacteristic
635C22×C42—591no—
636#386—24no—
637#386—1184no—
638#381—1184no—
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×#95—591no—
649C2×#95—591no—
650C2×#95—591no—
651C2×#95—591no—
652C2×#95—591no—
653C2×#95—591no—
654C2×#95—591no—
655C2×#95—591no—
656C2×#95—591no—
657C2×#95—1184no—
658C2×#95C2×D5911yescharacteristic
659C2×#95C2×D5911yescharacteristic
660C59#1389411yescharacteristic, complemented, Sylow
661C25C22×D5911yescharacteristic
662C25C22×D5911yescharacteristic
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—22no—
667C22×D4C4×D5914yes—
668C22×D4D23614yes—
669C22×D4C22⋊D5914yes—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—41no—
676C23×C4—41no—
677C23×C4—591no—
678C23×C4—591no—
679C23×C4—591no—
680C23×C4—591no—
681C23×C4—591no—
682C23×C4—591no—
683C23×C4—594no—
684C23×C4—594no—
685C23×C4—591no—
686C23×C4—591no—
687C23×C4—1182no—
688C23×C4—1182no—
689C23×C4—1182no—
690C23×C4—1182no—
691C23×C4—1182no—
692C23×C4—1182no—
693C23×C4—1182no—
694C23×C4—1182no—
695C23×C4—1182no—
696C23×C4—1182no—
697C23×C4—1182no—
698C23×C4—1182no—
699C23×C4—1182no—
700C23×C4—2361no—
701C23×C4—2361no—
702C23×C4—2361no—
703C23×C4—2361no—
704C23×C4—2361no—
705C23×C4—2361no—
706C23×C4C22×D5911yescharacteristic
707C23×C4C22×D5911yescharacteristic
708C23×C4C22×D5911yescharacteristic
709C23×C4C22×D5911yescharacteristic
710C23×C4C22×D5911yescharacteristic
711C4×D4—11832no—
712C2×C4⋊C4—594no—
713C2×C4⋊C4—1182no—
714C2×C4⋊C4—1182no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—594no—
725C2×C22⋊C4—594no—
726C2×C22⋊C4—1182no—
727C2×C22⋊C4—1182no—
728C2×C22⋊C4—1182no—
729C2×C22⋊C4—1182no—
730C2×C22⋊C4—1182no—
731C2×C22⋊C4—1182no—
732C2×C22⋊C4—1182no—
733C2×C22⋊C4—1182no—
734C2×C22⋊C4—1182no—
735C2×C22⋊C4—1182no—
736C2×C22⋊C4—1182no—
737C2×C22⋊C4—2361no—
738C2×C22⋊C4—2361no—
739C2×C42—594no—
740C2×C42—1182no—
741C2×C42—1182no—
742#95—22no—
743#95—22no—
744#95—594no—
745#95—1182no—
746#95—1182no—
747#95—1182no—
748#95—1182no—
749#95—1182no—
750#95—1182no—
751#95—1182no—
752#95—1182no—
753#95—1182no—
754#95—1182no—
755#95—1182no—
756#95—2361no—
757#95—2361no—
758#95—2361no—
759#95—2361no—
760#95—2361no—
761#95—2361no—
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—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24C2×C4×D5912yes—
783C24C2×C4×D5912yes—
784C24C2×D23612yes—
785C24C2×D23612yes—
786C24#1174568712yes—
787C24#1174568712yes—
788C24#1174568712yes—
789C24#1174568712yes—
790C24C2×C22⋊D5912yes—
791C24C2×C22⋊D5912yes—
792C24C23×D5911yescharacteristic
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4(C2×D59)⋊C4116yes—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—28no—
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—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—592no—
838C22×C4—592no—
839C22×C4—592no—
840C22×C4—592no—
841C22×C4—592no—
842C22×C4—592no—
843C22×C4—592no—
844C22×C4—592no—
845C22×C4—1188no—
846C22×C4—1188no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1188no—
852C22×C4—1188no—
853C22×C4—1188no—
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—1181no—
887C22×C4—1181no—
888C22×C4—1181no—
889C22×C4—1181no—
890C22×C4—1181no—
891C22×C4—1181no—
892C22×C4—1181no—
893C22×C4—1181no—
894C22×C4—1181no—
895C22×C4—1181no—
896C22×C4—1181no—
897C22×C4—1181no—
898C22×C4—2364no—
899C22×C4—2364no—
900C22×C4—2364no—
901C22×C4—2364no—
902C22×C4—2364no—
903C22×C4—2364no—
904C22×C4—2364no—
905C22×C4—2364no—
906C22×C4—2364no—
907C22×C4—2364no—
908C22×C4—2364no—
909C22×C4—2364no—
910C22×C4—2364no—
911C22×C4—2364no—
912C22×C4—2364no—
913C22×C4—2364no—
914C22×C4C2×C4×D5912yes—
915C22×C4C2×D23612yes—
916C22×C4D4×D5912yes—
917C22×C4#1174568712yes—
918C22×C4C2×C22⋊D5912yes—
919C4⋊C4—1188no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—1188no—
924C22⋊C4—1188no—
925C22⋊C4—2364no—
926C22⋊C4—2364no—
927C22⋊C4—2364no—
928C42—1188no—
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—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23C2×(C2×D59)⋊C414yes—
992C23C2×(C2×D59)⋊C414yes—
993C23#1427368314yes—
994C23#1427368314yes—
995C23#1427370814yes—
996C23#1427370814yes—
997C23#1427371114yes—
998C23#1427371114yes—
999C23C22×C4×D5911yescharacteristic
1000C23C2×D4×D5911yescharacteristic
1001C23C22×C22⋊D5911yescharacteristic
1002C23C22×D23611yescharacteristic
1003C23#41×D5911yescharacteristic
1004C23#41×D5911yescharacteristic
1005C23C2×#1174568711yescharacteristic
1006C23C2×#1174568711yescharacteristic
1007C23C2×#1174568711yescharacteristic
1008C23C2×#1174568711yescharacteristic
1009C23C2×#1174568711yescharacteristic
1010C23#1427377211yescharacteristic
1011C23#1427377211yescharacteristic
1012C23#1427377311yescharacteristic
1013C23#1427377411yescharacteristic
1014D4—232no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—416no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—594no—
1051C2×C4—1182no—
1052C2×C4—1182no—
1053C2×C4—1182no—
1054C2×C4—1182no—
1055C2×C4—1182no—
1056C2×C4—1182no—
1057C2×C4—1182no—
1058C2×C4—1182no—
1059C2×C4—1182no—
1060C2×C4—1182no—
1061C2×C4—1182no—
1062C2×C4—1182no—
1063C2×C4—1182no—
1064C2×C4—1182no—
1065C2×C4—1182no—
1066C2×C4—1182no—
1067C2×C4—1182no—
1068C2×C4—1182no—
1069C2×C4—1182no—
1070C2×C4—1182no—
1071C2×C4—1182no—
1072C2×C4—23616no—
1073C2×C4—23616no—
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—23616no—
1089C2×C4—2361no—
1090C2×C4—2361no—
1091C2×C4—2361no—
1092C2×C4—2361no—
1093C2×C4—2361no—
1094C2×C4—2361no—
1095C2×C4—2361no—
1096C2×C4—2361no—
1097C2×C4—2361no—
1098C2×C4—2361no—
1099C2×C4—2361no—
1100C2×C4—2361no—
1101C2×C4—2361no—
1102C2×C4—2361no—
1103C2×C4—2361no—
1104C2×C4—2361no—
1105C2×C4—2361no—
1106C2×C4—2361no—
1107C2×C4—2361no—
1108C2×C4—2361no—
1109C2×C4C2×(C2×D59)⋊C414yes—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—24no—
1125C22—24no—
1126C22—24no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22#1683726318yescomplemented
1140C22C22×(C2×D59)⋊C411yescharacteristic
1141C22C2×#1427368311yescharacteristic
1142C22C2×#1427368311yescharacteristic
1143C22C4×D4×D5911yescharacteristic
1144C22C4×#1174568711yescharacteristic
1145C22#1683787411yescharacteristic
1146C22#1683788111yescharacteristic
1147C22C2×#1427370811yescharacteristic
1148C22C2×#1427370811yescharacteristic
1149C22C2×#1427371111yescharacteristic
1150C22C2×#1427371111yescharacteristic
1151C22#1683790811yescharacteristic
1152C22#1683791211yescharacteristic
1153C22#1683792911yescharacteristic
1154C22#1683793311yescharacteristic
1155C22#1683798711yescharacteristic
1156C22#1683798911yescharacteristic
1157C22#1683799611yescharacteristic
1158C22#1683799711yescharacteristic
1159C22D4×C22⋊D5911yescharacteristic
1160C22D4×D23611yescharacteristic
1161C22#1683803911yescharacteristic
1162C22#1683804011yescharacteristic
1163C22#1683804611yescharacteristic
1164C22#1683804711yescharacteristic
1165C22#1683804711yescharacteristic
1166C22#1683805111yescharacteristic
1167C22#1683805611yescharacteristic
1168C22#1683805811yescharacteristic
1169C22#1683807511yescharacteristic
1170C22#1683808311yescharacteristic
1171C22#1683808911yescharacteristic
1172C22#1683809511yescharacteristic
1173C22#1683809511yescharacteristic
1174C22#1683810411yescharacteristic
1175C4—24no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—1184no—
1181C4—4721no—
1182C4—4721no—
1183C4—2362no—
1184C4—2362no—
1185C4—2362no—
1186C4—2362no—
1187C4—2362no—
1188C2—28no—
1189C2—44no—
1190C2C2×#1683726311yescharacteristic
1191C2#2142653611yescharacteristic
1192C2#2142672211yescharacteristic
1193C2D4×(C2×D59)⋊C411yescharacteristic
1194C2#2142692111yescharacteristic
1195C2#2142702311yescharacteristic
1196C2#2142703411yescharacteristic
1197C2#2142755411yescharacteristic
1198C2#2142755611yescharacteristic
1199C2#2142756911yescharacteristic
1200C2#2142757111yescharacteristic
1201C2#2142782711yescharacteristic
1202C2#2142782911yescharacteristic
1203C2#2142784211yescharacteristic
1204C2#2142784411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#386C2
socle, cosocleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC2×#386D59
hypocenterC59#13894
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16837263C2semidirect
4. C22×C59⋊#95C2semidirect
5. #21422365C2semidirect
6. #21422363C2semidirect
7. #21422343C2semidirect
8. #21422343C2semidirect
9. #21422320C2semidirect
10. #21422320C2semidirect
11. #21422319C2semidirect
12. #21422318C2semidirect
13. #21422318C2semidirect
14. #21422318C2semidirect
21. C2×D4×Dic59C4semidirect
78. C23×Dic59C2×C4semidirect
90. C2×C4⋊Dic59C2×C4semidirect
105. C2×C22⋊Dic59C2×C4semidirect
108. C2×C4×Dic59C2×C4semidirect
126. C59⋊#95D4semidirect
537. C22×C59#381semidirect
660. C59#13894semidirect
1139. C22#16837263semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic592
C2×#168372822
C2×#168372632
C22×C59⋊#952
#214223652
#214223632
#214223432
#214223202
#214223192
#214223182
C2×C59×#3862
#1389459